Publications
OF THE
American Economic Association
Vol. XI. No. 4. Pages 331-442.
Appreciation and Interest
A STUDY OF THE INFIvUENCE OF MONETARY APPRECIA-
TION AND depreciation ON THE RATE OF INTER-
EST, WITH APPLICATIONS TO THE BIMETALLIC
CONTROVERSY AND THE THEORY OF INTEREST.
BY
IRVING FISHER,
Assistant Professor of Political Science in Yale University.
AUGUST, 1896.
PUBLISHED FOR THE
American Economic Association
BY The Macmii,lan Company
NEW YORK
LONDON : SWAN SONNENSCHEIN & CO.
Hi
^ta--,.*/api^
Q-
537
Copyright 1896 by
American Economic Association
PRESS OF
Andrus & Church,
ithaca, n. y.
^
APPRECIATION
AND
INTEREST.
Digitized by the Internet Arciiive
in 2010 with funding from
The Library of Congress
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CONTENTS.
Part I. Thkory.
PAGE.
Chapter I. Introduction.
li. Does appreciation necessarily aggravate debts? . ... i
§2. Efforts to find a "just" standard i
I 3. Invariability of standard not essential 3
I 4. Bearing of the rate of interest on the subject .... 3
Chapter II. One year contracts.
I I. Foreseen and unforeseen appreciation or depreciation, 6
I 2. One year contract, numerical illustration 6
I 3. Formula connecting interest and appreciation .... 8
§4. Money as standard and as medium 11
Chapter III. More than one year.
I I. Confusion in separating interest and principal .... 12
I 2. Compound interest, five years 12
? 3. General formula I3
I 4. Partial payments, seven years i4
I 5. General formula 16
I 6. Special case • ^^
Chapter IV. Present value.
I I. Different modes of payment do not aflfect present value, 19
I 2. Illustration when interest is paid annually and princi-
pal redeemed at maturity 20
I 3. Case of perpetual annuity 21
^ 4. Formula ^^
Chapter V. Varying rates of appreciation.
I I. Numerical illustration 23
§ 2. Average rate of interest 24
? 3. Formula for varying rate of interest 26
^ 4. Formula for average rate of interest 26
I 5. Formula for average rate of appreciation 28
I 6. Practical application 28
Chapter VI. Zero and negative interest.
I I. Limits to rates of interest and appreciation 3°
I 2. Effect of hoarding 3^
I 3. Negative interest possible 32
I 4. Investment not necessarily checked by zero interest . 33
vi Contents [338
Part II. Facts.
Chapter VII. Introduction.
§ I. Objections 35
§ 2. Existence of foresight in general 36
Chapter VIII. Gotd atid paper.
§ I. General evidence 38
^ 2. United States currency and coin bonds 39
f 3. Extent of foresight in gold premium 41
? 4. Dangers of preceding method 44
Chapter IX. Gotd and stiver.
? I. India "rupee paper" and gold bonds 46
I 2. Extent of foresight in Indian exchange 49
§3. Upper limit of gold borrower's loss in England . . . 51
^ 4. Bearing of a rupee debt on Indian finance 52
Chapter X. Money and commodities.
§ I. Difficulties in comparing successive periods 54
I 2. Rate of interest as related to high and low prices . 54
§ 3. Rate of interest as related to rising and falling prices
in England 56
§ 4. Rate of interest as related to rising and falling prices
in Germany, France, and the United States .... 60
§ 5. Rate of interest as related to rising and falling prices
in silver standard countries 63
^ 6. Measurement of foresight for short periods 66
I 7. Error of Jevons, Price, and others 67
^ S. Measurement of foresight for long periods, in England 70
I 9. Lower limit of borrower's loss in England 71
§ 10. Loss on contracts made before 1873, ^'^ England ... 73
§11. Measurement of foresight for long periods, in America, 74
§ 12. Theory as to mode of adjusting rate of interest to
price movements 75
I 13. Credit cycles 76
Part III. Applications.
Chapter XI. The bimetallic controversy.
§1. Magnitude of debtor's loss 80
§ 2. Index numbers 81
? 3. Bimetallism could not correct losses 82
§ 4. Bimetallism would violate contracts 83
§ 5. Fallacy that we can predict further losses 85
^ 6. Bimetallism to secure stability in standard 86
Chapter XII. The theory of interest.
\i. "Real" and "nominal" interest, inadequate terms, 88
339] Contents.
vn
I 2. An absolute standard is individualistic 90
I 3. Interest varies with length of contract 91
§ 4. Multiple theory of interest 91
Appe;ndix. StatisticaIv Data.
§ I. Table of interest rates each year in seven countries . . 93
I 2. References to other statistics of the rate of interest . . 96
I 3. Index numbers of prices and wages 98
STATISTICAI. TABLES.
Rates of interest realized on United States "coin" and " cur-
rency " bonds from dates mentioned to maturity 39
Rates of interest realized on United States "coin" and "cur-
rency " bonds from dates mentioned to January i, 1879,
(date of Resumption) 42
Rates of interest realized on India gold and silver bonds from
dates named to maturity or in perpetuity 47
Rates of interest realized on India gold and silver bonds for
periods specified 5^
Market rates of interest in seven countries, in relation to high
and low prices ... 55
London rates of interest in relation to rising and falling prices, 59
Berlin rates of interest in relation to rising and falling prices . 61
Paris rates of interest in relation to rising and falling prices . 61
New York rates of interest in relation to rising and falling prices
and wages "^
Average bank rates in gold and silver standard countries before
and after the breakdown of bimetallism 64
Rates of interest in relation to rising and falling prices in Cal-
cutta, Tokyo and Shanghai 65
Number of cases in seven countries favorable and unfavorable
to the theory that rising and falling prices are associated
respectively with high and low interest 66
London market rates of interest in relation to rising and falling
prices, wages and incomes for long periods 7°
New York rates of interest in relation to rising and falling
prices and wages for long periods 74
Yearly average rates of interest on "money" in seven coun-
tries 94
Index numbers for seven countries 99
PREFACE.
The connection between monetary appreciation and the
rate of interest has received very scant attention from econ-
omists. The writer has been led to beUeve that this neglect
has somewhat retarded the progress of economic science and
the successful interpretation of economic history — in particu-
lar the monetary history of the last twenty years. The views
here put forward were first stated in brief before the Ameri-
can Economic Association at Indianapolis, December, 1895.
They differ radically from those expressed by Mr. Giffen and
many other eminent economists. For this reason it has been
necessary to make a statistical examination of all available facts
bearing on the subject. Such a study could not be properly
conducted without a definite economic theory as a starting
point. The idea on which this theory is founded appears to
have occurred independently to several writers, of whom Mr.
Jacob de Haas, Jr., of Amsterdam, seems most fully to have
realized its importance. To develop the theory in a quanti-
tative form, some simple mathematics have been employed.
With numerical illustrations at each step, it is hoped
that those to whom mathematics are distasteful will find few,
if any, impediments to easy reading. The mathematical
reader, on the other hand, may feel that the discussions are
too much encumbered by numerical illustration and detail ;
but these presentations are usually in such a form that they
can easily be passed over by those who find them superfluous.
The gist of the theory is contained in Chapter II, but its
statement would not be complete, nor the apparent objections
to it fully answered, without the discussions of Chapters
III-VI.
X Preface. [342
The writer is greatly indebted to the many persons whose
names are mentioned in the text, who have supplied him
with important facts and references ; also to Professor Sum-
ner for the privilege of consulting his collection of works on
banking ; to Professor Hadley, for valuable suggestions and
criticisms ; to Mr. Horace White for pointing out the im-
portant pamphlet of the eighteenth century mentioned in
Chapter I ; and to Mr. Sakata for translating several statis-
tical tables from Japanese.
New Haven, August, 1896.
PART I. THEORY.
CHAPTER I.
INTRODUCTION.
§1.
The chief issues in the bimetallic controversy center
about the question of justice between debtor and creditor.
The bimetallic propaganda succeeds just so far as it
spreads a belief that an injustice has been done by the
adoption of the gold standard, which the re-adoption of
bimetallism would correct.
The question therefore arises, does the appreciation of
gold necessarily aggravate debts? Are contracting
parties powerless to forestall the gains or losses of an
upward or downward moving currency ? It is clear that
if the unit of length were changed and its change were
foreknown, contracts would be modified accordingly.
Suppose a yard were defined (as once it probably was) to
be the length of the king's girdle, and suppose the king
to be a child. Everybody would then know that the
"yard" would increase with age and a merchant who
should agree to deliver i,ooo " yards " ten years hence,
would make his terms correspond to his expectations.
To alter the mode of measurement does not alter the
actual quantities involved but merely the numbers by
which they are represented.
§2.
Hitherto monometallists have usually replied to the
argument "gold has appreciated, therefore the debtor
2 American Economic Association. [344
has been robbed " by challenging, not the inference, but
the premise. Thus the discussion has been shunted off
from economic theory and turned into a controversy
over the fact of "appreciation." This controversy has
been, to a large extent, a mere war of words, because, by
" appreciation " the monometallists mean one thing and
the bimetallists, another. No one has ^-et provided a
meaning for that much abused word acceptable to both
parties. The bimetallists prove the appreciation of gold
by the fall in prices. The monometallists reply that
wages have risen, and hold that the fall in prices is due
to progress in the arts. Some bimetallists, e. g.^ Leonard
Courtney,^ accept the distinction between a fall in prices
through causes connected with gold and a fall through
causes connected with commodities, but most of them
assert that a " fall of prices " and " appreciation of gold "
are synonymous expressions, and that, if progress cheap-
ens other commodities, it ought justly to cheapen gold
also. Generally speaking, bimetallists set up the " com-
modity standard " and monometallists, the " labor
standard."
Others attempt to find the "just" standard in "mar-
ginal utility," " total utility," and so forth. On all sides
it is tacitly assumed that a "just" standard must in
some sense be an " invariable " standard ; that is, a
standard such that the principal of the debt when due
should be equivalent in some way to the original loan.
" All writers on the subject of money have agreed that
uniformity in the value of the circulating medium is an
object greatly to be desired — a currency to be perfect,
should be absolutely invariable in value." " Proposals
1 Report of the Indian Currency Committee, 1S93, p. 39; also,
Nineteenth Century, April, 1893.
^ Ricardo, "Proposals for an Economic and Secure Curreuc}',"
Sees. I, II.
345] Appreciation and Interest. 3
to define and secure such invariability have been made
by many writers. Within the last few years, the prob-
lem has become a favorite one and scarcely an issue of
the economic journals appears without discussions on
" The ultimate standard of value," " The just standard
of deferred payments," " Has gold appreciated ? " " The
measurement of the value of money," and kindred sub-
jects.^
§3.
It is not prosposed to deny that the terms appreciation
and depreciation may have an " absolute " as distinct
from a " relative " meaning.^ But such definitions and
distinctions can throw no light whatever on the question
of justice in contracts. We shall see that a standard to
be perfect need not be invariable. What is required is
simply that it shall be dependable^ so that contracting
parties may be able to forecast all required elements of
their economic future in terms of that standard as accur-
ately as in terms of any other. If a standard is thus de-
pendable, the terms of the contract will be as "just" as
they could possibly be under any system.
§4.
At a later stage the general question of " justice " will
be discussed. Here the effort will be to show that losses
due to " appreciation," however defined, will tend to be
forestalled. For this, it is not necessary to scale the
principal of a debt. The principal is not the only or
even the chief element in a loan contract. The other
element is the rate of interest. It is an astonishing fact
^See, e. g., the connected discussions in the Annals of the Ameri-
can Academy of Political and Social Science, 1892-95, and the fournal
of Political Economy, 1893-95, by Ross, Merriam, Fetter, Commons,
Newcomb, Cummings, Orton and Taylor.
* See Chapter XII.
4 A7nerica7i Economic As,sociation. [346
that tlie connection between the rate of interest and ap-
preciation has been ahnost completely overlooked, both
in economic theory and in its bearing upon the bime-
tallic controversy.
Of the few writers who have conceived this connection,
apparentl}^ the earliest was the anonymous author of the
remarkable pamphlet entitled : " A Discourse Concerning
the Currencies of the British Plantations in America."
Boston, 1740 (Reprinted in the " Overstone Tracts,"
1857). He writes :
The ArgU7nents current atnongst the Populace in favour of Paper
Money, are,
I. lu most of the Paper Money Colonies one of the principal Rea-
sons alledged for their first Emissions ; was, to prevent Usurers impos-
ing high Interest upon Borrowers, from the Scarcity of Silver Money.
It is true, that in all Countries the increased Quantity of Silver, falls
the Interest or Use of Money ; but large Emissions of Paper Money
does naturally rise the Interest to make good the sinking Principal : for
Instance, in the Autumn, A. 1737, Silver was at 26 s. to 27 s. per Ounce,
but by a large Rhode Island Emission, it became in Autumn 1739, 29 s.
per Oz. this is 7 per Cent. Loss of Principal, therefore the Lender, to
save his Principal from sinking, requires 13 per Cent, natural Interest
(our legal Interest being 6 per Cent.) for that Year. In Autumn A.
1733, Silver was 22 s. per Oz. by large Emissions it became 27 s. in
the Autumn, A. 1734 ; is 22 per Cent, loss of Principal ; and the
Lender to save his Principal ; requires 28 per Cent, natural Interest
for that Year. Thus the larger the Emissions, 7iatural Interest be-
comes the higher ; therefore the Advocates for Paper Money (who are
generally indigent Men, and Borrowers) ought not to complain, when
they hire Money at a dear nominal Rate.
If Bills were to depreciate after a certain Rate, Justice might be
done to both contracting Parties, by imposing the Loss which the
Principal may sustain in any certain Space of Time (the Period of
Payment, upon the Interest of a Bond or Price of Goods : biit as De-
preciations are uncertain, great Confusions in Dealings happen.
John Stuart Mill expresses the same view,^ as do
^ "Principles of Political Economy," Book 3, Chapter 23, \ 4. [A
single paragraph.]
347] Appreciation and hiterest. 5
also Jacob de Haas^ and Professor John B. Clark.^ A
principle which apparently has been independently dis-
covered by each of these economists and quite possibly by
others, is likely to be of some importance. It is the ob-
ject of the present essay to develop the theory in a quan-
titative form, to bring it to a statistical test, and to apply
it to current problems, and to the theory of interest.
^ " AThird Element in the Rate of Interest." Journal of the Royal
Statistical Society, March, 1889. [A more extended discussion, with
statistics.]
2 " The Gold Standard in the Light of Recent Theory." Political
Science Quarterly, September, 1895. [Applied to the current bime-
tallic controvers}'.]
CHAPTER 11.
ONE YEAR contracts/
§1.
We must begin by noting the distinction between a
foreseen and an nnforeseen change in the value of money.
Only the losses or gains of the former can be forestalled.
A sudden and unexpected inflation, as in the United
States in 1862, works enormous losses to creditors while
an unforeseen contraction is equally harmful to debtors.
How far foresight in such matters actually exists will
be discussed in Part II. At present we wish to discover
what will happen, assumiJig this foresight to exist.
If a debt is contracted optionally in either of two
standards and one of them is expected to change with
reference to the other, will the rate of interest be the
same in both ? Most certainly not. Only a few months
ago the Belmont-Morgan syndicate offered the United
States government the alternative of taking some 65
millions at 3/^ in gold or at 3^/^ in "coin." Every-
one knew that this additional ^ ^ was due to the mere
possibility of free silver coinage. If the alternatives had
been between repayment in gold and — not possible but
actual — repayment in silver, the additional interest
would certainly have been much more than 3/^ f/c .
§2.
To fix our ideas, let the two standards be gold and
wheat, and, while today a bushel of wheat is worth a
' More properly speaking, in place of "one j^ear " should be put
" one interest interval."
349] Appreciation and Interest. 7
dollar, let it be known that one year hence it will be
worth bnt 96 cents. One hundred dollars (gold standard)
or its equivalent one hundred bushels (wheat standard)
are borrowed today and are to be repaid with interest in
one year. If the rate of interest in the gold standard is
8 'fo , what will be the rate in wheat ?
We note that the repayment, if in gold, will be, not
$100 but $108, and our problem is solved by finding
what will be the equivalent of this sum in wheat at the
end of the year. This is easily obtained from the ex-
pected price of wheat, thus : ^
96 cents gold =«= i bushel wheat.
Hence i dollar " — ^i- bushels " i. e., \.o\\\>Vi.
loS dollars " — loS X 1.04I bushels " i. e., 112^ bu.
Thus the repayment of 1 1 2^ bushels will be equivalent
to $108. The alternative contracts would tl\erefore be :
\
For 100 dollars borrowed today, 108 dollars are due one year hence.
For 100 bushels " " 112 J bushels " " "
Hence 8 fo interest in the gold standard is equivalent
to 12^% in the wheat standard.
Now the relative change in the two standards may be
spoken of either as an appreciation of gold relatively to
wheat or as a depreciation of wheat relatively to gold.
We are not compelled to inquire which is the "abso-
lute" change. If we speak in terms of appreciation, we
say $1 changes in value from i bushel of wheat to 1.04%
bushels and hence has appreciated 4}i'/o ] while we may
also say, wheat has depreciated from ^i to $.g6 or 4^.
Our results can be stated in either of two ways :
I. If the rate of interest in one standard is 8^, then
in another, which depreciates 4 fo relatively to the first,
it will be 12 }4fo ; that is, a depreciation of 4^ is offset
by an increase of interest of 4}^ fo.
1 The symbol " =0= " is used for " are equivalent to."
8 American Economic Association. [350
2. If the rate of interest in one standard is 12)^ %, in
another, which appreciates 4 ^-^ /^ relatively to the first,
it will be 8 ;% ; that is, an appreciation of 4 )^ ^ is offset
by a decrease of interest of 4j^ /^.
§3.
Leaving this numerical case, we may state the problem
more generally. Suppose gold is to appreciate relatively
to wheat a certain known amount in one year. What
will be the relation between the rates of interest in the
two standards ? Let wheat fall in gold price (or gold
rise in wheat price) so that the quantity of gold which
would buy one bushel of wheat at the beginning of the
year will buy 1 -\- a bushels at the end, a being therefore
the rate of appreciation of gold in terms of wheat.
Let the rate of interest in gold be z, and in wheat be
y, and let the principal of the loan be D dollars or its
equivalent B bushels.
Our alternative contracts are then :
For D dollars borrowed D-\-D i or D { i-\-i) dollars are due in one yr.
For ^bushels " i5 f 5/ or ^ ( i+y) bushels " " " "
and our problem is to find the relation between i and/,
which will make the Z>(i + 2) dollars =g= the B (1 -]-j)
bushels.
At first, D dollars - B bu.
At the end of the year Z> " ^ B {\+a)
Hence " " " Z>(i+?) " =0= i? ( i-f rt) (1 + /) "
Since Z)(i + i) is the number of dollars necessary to
liquidate the debt, its equivalent B {1 + a) (i + 2) is the
number of bushels necessary to liquidate it. But we
have already designated this number of bushels by
Our result, therefore, is :
35 1] Appreciation and Interest. 9
Dollars. Bushels. Buishels.
At the end of i yearZ?(r + /) ^ B {\ -^j) = B {\ -\- a) {\ ^ i) (i)
which, after B is canceled, discloses the formula :
i+y=(i+«) (i+o (2)
or j=--^^-a-\-ia (3)
or in words : The rate of interest in the (^relatively) de-
preciating standard is equal to the sum of three terms^
vis.^ the rate of interest in the appreciatittg standard.,
the rate of appreciation itself and the prodicct of these
two elemeiits.
Thus, to offset appreciation, the rate of interest must
be lowered by slightly more than the rate of apprecia-
tion/
We may introduce depreciation in a similar manner.
Instead of saying, gold appreciates at the rate «, rela-
tively to wheat, we may say, wheat depreciates at the
rate (f, relatively to gold.^ This means that wheat has
sunk in terms of gold in the ratio i to i — ^, and rea-
soning similar to the foregoing shows that
i4-^ = (i-^)(i+y). (4)
Equations (2) and (4) may be conveniently combined,
thus :
i + « I i—d' ^^'
'Professor Clark, {Political Science Quarterly, September, 1895),
implies that i % appreciation is offset by less than i % reduction of
interest. But in making his calculation he has failed to "compound."
The numerical illustrations of the eighteenth century pamphleteer
{supra) are also erroneous. E.g., instead of 28 %, should be 29.32
%. Professor Marshall, (" Principles of Economics," Vol. T, 3rd ed.,
p. 674), gives a correct example. His example is designed to show
the losses from a fluctuating currency and not the effort to offset these
losses. He appears, however, to have in mind this effort when he
postpones to the next volume the discussion of " the influences which
changes in the purchasing power of money do actually exert on the
terms on which loans are arranged," (p. 673).
■■^ The relation between rfandais (i+a) (r— ^) = i, which is evi-
dent from equation (5) or can be easily shown independently.
lo Amej'icaji Economic Association. [352
Since ' — is the ratio of the vahie of gold at the end
of the year to its vahie at the beginning (all in terms of
wheat), that is, the ratio of divergence of the two stand-
ards expressed in wheat, while is the same ratio
I — d
of divergence expressed in gold, and since i + i is the
" amount " of $1 put at interest for one year while i +7
is the " amount " of one bushel ; we may state equation
(5) as follows :
The ratio of divergence betiveen the standards equals
the ratio between their " ainoiints^
■ This is, perhaps, the simplest mode of conceiving the
relation and stress is laid upon it because it brings into
prominence the " amount," or ratio of future payment to
present loan, a magnitude which in most questions of in-
terest plays a more important role than the rate of in-
terest itself/
Equation (5) gives the relation between i and / in
terms of a or d. From it, follows the value of/ in terms
either of i and a or of i and d^ and also the value of i in
terms either of y' and a or of y' and <^, thus :
I + ^ I 1 — a
whence j =:i -\- a -\- i a -^ (6)
I — d
or i =j — d —j d ^~-^ ( 7 )
I -r a
^ In fact, except for convenience in computation, the conception of
the rate of interest might well be dispensed with, giving place to the
conception of a year's "amount" or "ratio of accumulation." In
his "Positive Theory of Capital," Professor Bolim-Bawerk expresses
the same view. (English Translation, p. 296). We should then speak,
not of a 6 % rate of interest, but of 1.06 as the " ratio of accumula-
tion." In like manner " rate of appreciation " would give place to
" ratio of appreciation." Denoting the ratio of accumulation, i -\- j,
by r^ and i + ^ by r, and the " ratio of appreciation," i -p a, by />, our
theorem becomes simply - =/>.
r
353] Appreciation and Interest.
II
It follows that j exceeds i by more than the rate of
appreciation, which in turn is more than the rate of de-
preciation, {i. e.^j — i^ ay> d).
§4-
It is to be noted that we have been regarding money
as a standard of value and not as a medium of exchange.
In either contract the actual liquidation need not be
made either in gold or wheat but in some other medium,
as bank notes. The speculator who sells wheat " short,"
really uses wheat as a standard and not necessarily as a
medium. In consideration of value received today
(which, though reckoned by the speculator in money,
may readily be thought of as measured in wheat) he
promises to deliver, at a later date, so many bushels of
wheat, it being perhaps understood that he need not act-
ually deliver the wheat so long as he delivers its equiv-
alent in money. This operation, as actually practiced,
involves great uncertainties, and therefore occurs as a
gambling transaction. Moreover the wheat is not
usually paid for in advance. But if wheat were a more
reliable standard, selling it " short " in consideration of
present advances might be a true method of business
borrowing, and would then exactly exemplify the case
we have supposed. In fact, such contracts are identical
in form with those which would be made under the
oft-proposed " multiple standard."
CHAPTER III.
MORE THAN ONE YEAR.
§1.
A prominent bimetallist in conversing with the writer
on the subject of interest and appreciation, raised the
following objection: "Interest and principal are sepa-
rate ; the one is paid regularly in installments ; the other
remains to the end ; hence appreciation must affect them
in totally different ways. I do not see how it is possible
by a uniform reduction in interest applied to contracts
of different periods to offset the appreciation of both
interest and principal." This view, as we shall soon
see, is quite erroneous and arises from the habit of
separating in thought interest and principal.
First consider the case in which no interest is paid
until the end of the term of years. Let us suppose,
for instance, a savings bank which receives $ioo, gold
standard, and repays the depositor in five years at 5 ^
compound interest. If there were an alternative
standard, say wheat, in terms of which gold is known to
appreciate ^ constantly by i ^ per annum, what would
be the rate of interest in this standard ? We shall sup-
pose for convenience that at first the price of wheat is
$1 per bushel.
^ Or what is equivalent, wheat depreciates ygx^ relatively to gold.
As it will be understood that there are always these two modes of ex-
pressing the relative change of two standards, we shall hereafter
adhere to "appreciation."
355] Appreciation and Interest. 13
If the repayment were to come in one year, we know
from Chapter I, § 3, that the rate of interest in wheat is
given by the formula
j^i-{-a-\-ta
= .05 + .01 +.0005
= .060^
This result is as truly the answer to our problem for a
series of years as for one year. The proof consists
simply in separating the contract into several contracts
of one year each. Thus, by Chapter II, we know if we
deposit today 1 100 or its equivalent, 100 bushels, it will
amount in i year to $105 at 5;^ or its equivalent, 106.05
bushels, at 6^^o. We may now regard these equiv-
alent amounts as withdrawn but immediately redeposited
for one year. Then, with the same rate of interest in
gold and the same rate of relative appreciation, we shall
obtain the same rate of interest in wheat, so that $105.00
or its equivalent, 106.05 bushels, will amount in i year
to I110.25 ^t 5^, or its equivalent, 112.47 bushels at
6-^^. In this way each successive pair of " amounts,"
including the last, will be equivalent.
The principle employed in § 2 is to resolve the contract
into a series of one year contracts. The general case is
precisely similar. For the first year we have, by
formula (i). Chapter II,
Dollars due. Bushels due. Bushels due.
D{i + i)<^B{i+j)=B{i + a){i-\-i)
In the second year the same formula applies except
that in place of Z?, the principal is now Z> (i + 2), and
in place of B, B (i +/) or ^ (i + a) (i + i). Making
these substitutions in the formula, we obtain
l>[\ iV -^ /.\i , ,/y /*(i I aY [i ! i'Y
A\\<\ similuK in tlu- thli\l year,
aiul sv» vMi. Kach of the results discloses the priuoiple
1\\ §$ J i\iv*.l ^^> we began for simplicity with the case
in which the debt is allowetl to accmuulate to the end.
The most general ease, however, is one in which the re-
|x^yn\ents are in installments.
Suppose, as in § 3, that the interest in gold is 5 '/c and
that gold is known to appreciate i % per annum rela-
tively to wheat. A fanner mortgages his land for $i.ckx>
oar its then e<jnivaleut, i>ooo bushels of wheat, and agrees
to pay annually the interest and such parts of the principal
as he can save, tnaking the repayment complete in 7 years.
Our problem is to find that rate of interest in wheat
which will make the contracts in gold and wheat
e<^uivaleut iu every respect.
The solution of this problem is precisely the same as
that of § 2, viz., 65^ %, For. at the end of one year, the
farmer's debt amounts to $1050 or its then equivalent,
io6<X50 bushels, Let us suppose that he finds himself
aUeto pay, not only the ^4nterest>" $50, but also $50 of
the ^' principal,' * that is $100 altogether. The equi\^
lent of this iu wheat is ici. 00 bu.
Hence he cart either
pay $ic>o,<x> oa $1,050,00, leavnng $95aoo
or 101,00 bu, Qu. 1,060^50 bu., leaving 959^ 50 bn.
aod, since the ^"amounts" $1,050 and 1,060,50 bu, are
e^ilu\^ilent and the deductions; $ioo and ioi,oo bu, are
557]
Appreciation and Interest.
15
equivalent, the remainders $950 and 959.50 bu. must also
be equivalent ; and, in fact, this may be seen directly
since, with gold appreciating i ^ , $950, originally worth
950 bu., becomes worth i ^ more, or 959.50 bu.
Thus the farmer's remaining debt at the end of the
first year is the same whether measured in wheat or
gold and since the same reasoning applies to the second
year, third year, etc., the equivalence remains to the end
of the contract.
It is worth noting here that the $100 payment in gold
will be regarded as consisting of half interest and half
principal, whereas the equivalent payment in wheat,
101.00 bu., consists of 60.50 bu., interest and 40.50 bu.,
principal.
The liquidation of the contract during the 7 years
may be supposed to take place in either of the following
equivalent ways :
GOLD STANDARD.
I
Interest. 1 Amount.
Paj-ment.
Prixicipal.
At beginning
|i,ooo.oo
950.00
900.00
800.00
690. 00
550.00
300.00
0.00
In I year
In 2 years
':\i ■::■:■:■.
"6 "
"7 "
I50.00
47-50
45.00
40.00
34-50
27.50
15.00
^1,050.00
997-50
945.00
840.00
724-50
577-50
315-00
|ioo.oo
97-50
145.00
150.00
174-50
277-50
315-00
WHEAT STANDARD.
Interest.
Amount.
Paj-ment.
Printripal.
At beginning
1,000.00 bu.
In I year
In 2 years
"3 "
"4 "
'•5 "
"6 "
"7 "
60.50
58.05
55 54
49-87
43-44
34-97
19.27
1,060.50
1,017-55
973-63
874- 1 1
761.46
61303
337-73
101.00
99.46
149-39
156.09
183.40
294-57
337-73
959-50 "
91S.09 "
824.24 "
718.02 "
57S.06 "
318-46 "
0.00 "
In these two tables ever}- entrs" in one is equivalent to
i6 American Economic Association. [358
the corresponding entry in the other except those in the
interest columns.
We thus see that the farmer who contracts a mortgage
in gold is, if the interest is properly adjusted^ no worse
and no better off than if his contract were in a " wheat "
standard or a " multiple " standard.
§5-
The principle involved in § 4 is that equivalent pay-
ments subtracted from equivalent " amounts " will leave
equivalent remainders. The payment in any year forms
the same fractional part of the " amount " in the two
standards. We may designate this fraction at the end
of the first year by y^ the second year by _/', etc., and
we have the following results :
END OF FIRST YFAR.
Dollars. Bushels. Bushels.
Amount. i?(i+/)* ^(i+y)= ^ (1+^) ( i-|./)
Paym't f D {\^i) -^ fB{i-^j)= f B {\^a) (i+z)
R'md'r . (I-/) Dii^i) <^ (i-/) B{i^j ) = (i-/) B{x^a) (1+/)
In like manner the unpaid remainder at the end of the
second year can be shown to be
Dollars. Bushels. Bushels.
(I-/') (I-/) D (1+0= * (I-/') (I-/) B (i+y)2= (I-/') (I-/) B (i+ar- (1+02
and so on for any number of years. Each result again
yields the formula (i +/) = (! + «) (i + z).
This includes, of course, the case of § i, in which no
partial payments are made,y^y"', etc., being then zero.
§6.
One special case may seem to require separate consid-
eration. Suppose the interest alone is annually paid and
the principal redeemed at the end, as in the case of a
bond not subject to a sinking fund. What correspond-
ence between the two standards is then possible ? The
following tables answer this question, the first, for the
359]
Appreciation and Interest.
17
case where the wheat interest, the second, where the
gold interest is annually paid.
TABLE I.
TABI,E II.
Interest.
Amount.
Payment.
Principal.
At beginning (Bushels^
1,000.00
In I year . . . '
•
60.50
1,060.50
60.50
1,000.00
" 2 years. .
" 3 "
«' 4 '«
" 5 "
« 6 <<
" 7 "
" 8 "
" 9 "
'
" 10 "
1,060.50
0.00
At bep^inning (Doll^i's^
1,000.00
In I year . . . '
'
50.00
1,050.00
59-90
990. 10
' ' 2 years . .
49-50
1,039.60
59-31
980.29
" 3 "
.
49.01
1,029.30
58.72
970.58
" 4 '•
48.53
1,019.11
58.14
960.97
" 5 "
48.05
1,009.02
57.56
951.46
" 6 "
.
47-57
999.03
56.99
942.04
" 7 "
47.15
989.19
56.43
932.76
" 8 "
46.63
979-39
55.87
923.52
<< g .<
46.17
969.69
55.32
914.37
" 10 "
•
45-71
960.08
960.08
0.00
At beginning (Busi
In I year . . . '
lels)
1,000.00
60.50
1,060.50
50.50
1,010.00
" 2 years.
' 61.10
1,071.10
51.00
1,020.10
"3 " •
' 61.72
1,081.82
51.52
1,030.30
"4 " .
62.32
1,092.62
52.03
1,040.59
"5 " •
' 62.96
1,103.55
52.55
1,051.00
"6 " .
63.59
1,114-59
53-08
1,061.51
"7 " .
' 64.22
1,125.73
53-61
1,072.12
"8 " .
64.86
1,136.98
54.14
1,082.84
"9 " .
65.51
1,148.35
54.68
1,093.67
" 10 " .
66.17
1,159.84
1,159.84
0.00
At beginning (Del
In I year . . . '
lars)
1,000.00
' 50.00
1,050.00
50.00
1,000.00
" 2 years.
"3 " •
"4 " .
"5 " •
"6 " .
<
"7 " .
"8 " .
"9 " .
" 10 " .
( ((
1,050.00
0.00
1 8 America7i Economic Association. [360
From Table I, it will be seen that the case in the
wheat standard, in which only the interest is annnally
paid and the principal redeemed in ten years is equiva-
lent, step for step, in the gold standard to a series of
small partial payments. Thus, instead of paying merely
the annual interest of I50, the sum paid the first year is
$59.90 reducing the principal by $9.90. At the end
there is due I914.37 of principal and $45.71 of interest,
making $960.08 in all, which at that date is, of course,
precisely equivalent to the 1,060.50 bushels, the final
payment in wheat.
On the other hand, the case in which the gold interest
payments are kept up, corresponds to a series of wheat
payments less than the annual interest, so that the un-
paid interest accumulated to the end makes the sum then
due, 1,159.84 bu., of which 1,093.67 bu. are principal.
It is thus clear that the case in which in one standard
the interest is paid annually and the principal at the
end, can be exactly matched in the other standard either
by minute partial payments or minute arrears of interest.
Without such partial payments or arrears in one of the
standards, the two would not be equivalent step for step.
We shall see, however, that they would still be equiva-
lent as a whole.
CHAPTER IV.
" PRESENT VAI^UE."
In practice, of course no such minute partial payments
of principal or minute remissions of interest would be
made. Any advantages to be derived from such calcula-
tions of trifles would not be worth the trouble. But
even if we destroy the precise step-for-step equivalence
between the wheat and gold tables, we do not destroy
their equivalence as a whole. The '•^present values "
remain exactly equal.
The ordinary definition of the " present value " of a
given sum due at a future date is " thai sum which put
at interest today will ' amount ' to the given sum at
that future date." " Present value " and " amount " are
thus correlative terms. In fact we may extend the pre-
ceding definition to include the present value of past
sums as the accumulated " amount " today of the past
sum put at interest then.
The literal meaning of " present value " implies that
it is the actual market price today of a future sum due.
This is, in fact, the case. We need not stop to prove it
in theory, for we are all familiar with it in practice.
Elaborate tables are constructed on this principle for the
practical use of insurance companies in calculating their
premiums, and for brokers in determining the compara-
tive merits of various bond investments. What we are
here concerned with is applying the principle to our
problem.
20 A7ficrican Ecoyiomic Association. [362
§2.
If a debt of $1,000 is contracted today, interest being
5^, the "present value" of all payments, principal and
interest, by which that debt is to be liquidated is exactly
$1,000.^ Again, the debt's present value, reckoned at a
later date than the time of contract, is the " amount " of
$1,000 at interest from the time of contract to that date,
and this is true, whether or not any of the debt has al-
ready been paid. Thus if the present values at the date
of contract are computed for the gold and the wheat
debts of the last chapter, they will be $1,000 and 1,000
bushels, which are then equivalent. If the present val-
ues one year later are taken they are $1,050 and 1060.50
bushels which at that date are also equivalent, gold hav-
ing appreciated i fo .
From these familiar principles, it follows that the
present values of the two debts, reckoned at any date
whatever, are identical whether the individual payments
correspond or not. Thus, to take the case first referred
to, suppose the wheat debt to be discharged as in Table I
and the gold debt, as in Table II. The present value, at
the date of contract, of the interest and principal, sepa-
rately computed, will be •?
Dollars. Bushels.
Present value of all interest payments . . . , 386.09 < 444.24
" " principal due in 10 years . . 613.91 > 555.76
" " total 1000.00 "^ 1000.00
If the present values (including " amounts " of past
' This and the other general theorems on present value are not proved
here because their proof is accessible in most treatises on interest, an-
nuities, insurance, etc. See, e.g., the "Encyclopaedia Britannica,"
" Annuities."
'^ The symbol < is here used for "is less than the equivalent of "
and > for "is more than the equivalent of."
363] Appreciatio7i and Interest. 21
interest) were computed 5 years after the date of the
contract, the items would be :
Dollars. Bushels.
Interest 492-75 < 595-88
Principal 783-53 > 745-5°
Total 1276.28-1341.38
We thus see that it would be just as much a hardship
to pay the high interest in wheat as to pay the more
onerous principal in gold,
§3-
The case of a perpetual annuity may be given special
consideration. As is well known, the present value of a
perpetual annuity is its " capitalized " value. Thus, if
the rate of interest is taken at 5 ^ , the present value of
a perpetual annuity of $50 per annum is $1,000. Ap-
plying the same principle to the wheat annuity of 60.50
bushels and extending the previous reasoning, we find
that the two annuities are equivalent.
At first sight this seems impossible since 6-^ ^ is a
higher rate of interest than 5^. This is true in the
numerical sense, and it is also true that the early pay-
ments of 60.50 bushels are actually more valuable than
$50. But after a certain time (in this case 19 years) the
reverse is true. The 19th payment of $50 in gold is
worth 60.40 bushels while the 20th is worth 61.01 bush-
els. That is, the recipient of the wheat annuity has at
first a slight advantage over the recipient of the gold
annuity which ceases and becomes a slight disadvantage
after 19 years.
§4.
To derive the formula for the time at which the rela-
tive values of the two annuities become reversed, let the
rate of interest in gold be z, in wheat,/; let the two an-
22 American Economic Associatio7i. [364
nuities be D i and B j^ their capitalized values being D
and B [D =c= ^ at the beginning) and let x be the num-
ber of years in which BJ is as valuable as or more val-
uable than D i. Then
Bushels. Dollars.
At end of x years, - - - B j > Di
At end of .r + i years, - B j < Di
and since we know that in x years, D ^ B {\ ^- a)' and
hence Di o- Bt(i ^ a)'] and likewise in .r + i years,
Di =0= B i{\ + cl)""^^ ^ we see that the previous inequal-
ities become :
Bushels. Bu.shels.
At end of x years, - Bj > Bi(i ^ aY
At end of ;i; + i years, Bj < Bi{i -\- <^)-^+ '
which may be combined in the formula :
i (i +aK^y <i (i +«)^+ I
^<log/^log^ ^_^^_ (8)
— log(i+a)
That is, X is the integral part of the number
log J — log t
log (I +«)■
Thus, if 2^.05, a = .01, and hence also/ =.0605,
then
logy — log z_ 2.7818 — 2.6990 .0828
log ( I + a) .0043 "~ .0043 ~
Hence x = ig.
CHAPTER V.
VARYING RATES OF INTEREST AND APPRECIATION.
§1.
Hitherto we have assumed that the appreciation pro-
ceeded (during the period of the contract) at a constant
percentage rate per annum, and that the rate of interest
(in one standard, and consequently in the other) remained
constant also. The more general case is one in which
these elements are changing.
Beginning with a numerical case, let us suppose that
the United States government is offered an alternative
loan, not in gold or " coin," but in gold or silver. Let
it be known that lOO gold dollars will remain at par the
first year, but in two years will be worth 150 silver dol-
lars, that is, gold will " appreciate," in the second year,
50 ^ relatively to silver ; also that in the third and
fourth years it will appreciate 10 fo and 5^ respectively.
We shall suppose that the rate of interest, if the con-
tract be in gold, is 3 ^ for each year of the contract.
Our problem is to discover what will be the interest
in silver. It is perhaps already evident that it will be a
different rate for each year. If the contract were made
for one year only, the rate of interest in silver would
also be 3 ^ , since silver remains so far at par with gold.
If the contract (or any unpaid part of it) were then re-
newed for a second year, the rate of interest would be,
by formula (3) :
j = z -\- a-\- ai
= .03 + .50 + -015
= .545
= 54i%
24 American Economic Association. [366
In like manner, we may deduce the rate of interest in
each year, with the following results :
Gold Silver Appre-
Standard. Standard. ciation.
istyear ...... 3% 3 % 0%
2d year 3 54^ 50
3d year 3 13^ 10
4ttiyear 3 SyVj 5
Etc.
The question arises, can a single " average " rate of
interest be substituted for the above irregular series ?
We answer that such an average is not possible if the
debtor has the option of arbitrary partial payments.
If, for instance, the average were 20^, and the govern-
ment could pay ofi at any time, it would evidently be
tempted to refund the debt at the end of the second
year, to which the lending syndicate would not agree.
If, however, the conditions as to repayment are stipulated
for in advance, an average can easily be computed on the
principle of present values.
Suppose the government agrees to extinguish the
debt in four years by paying at the end of successive
years 20, 40, 30, and 10 millions (these to include " in-
terest"). The present value of these sums is 66.321
millions, which is therefore the amount of the loan re-
ceived from the syndicate. This sum is obtained by
adding the present values of several payments. The
present value of 20 millions, due one year hence, is
^° = 19.418 millions.
1.03
and of 40 millions, due two years hence, is
• ~ = 25.136 millious,
(1.03) (1.545)
for evidently if this be put at interest for one year at
367] Appreciation and Interest. 25
3^, and the next at 541-% it will amount to 40 millions.
Likewise the third and fourth payments have present
values of
-. ,, ^° ,, r = 16.639 millions
(i.03)(i.545)(i.i33)
5.128 millions.
(i.03)(i.545)(i.i33)(i.o8i5)
The sum of these four present values is 66.321 mil-
lions. Now if we compute the present values of the
four payments on the basis of a uniform rate of 20.26%
interest, we obtain the same sum, thus
r= 16.631 millions
(1.2026)
40
(1.2026^
30
27.659
^ = 17-250
( 1. 2026)''
^° = 4-781 "
(r.2026)*
Total, =66.321 "
The separate present values are here fictitious, that is,
no one of them is the actual present selling price of the
future payment to which it refers, but the deviations so
offset each other that their sum is the actual present
selling price of the whole set of future payments. It
follows from principles already stated that the debt,
66.321 millions, can be liquidated by precisely the same
payments (20, 40, 30 and 10 millions) whether the in-
terest is reckoned separately at 3, 54^, i3to", ^^^ ^tot^
or uniformly at 20.26%. In fact the details of the book-
keeping in the two cases are :
26
American Economic Association.
[368
At 3, 54i i3T^ff. StVc^-
At 20.26% uniformly.
(In Millions.)
(In Million.?.)
I'^ter- ^^o„„t
Pay-
ment.
Prin-
cipal.
Inter-
est.
Amount.
Pay-
ment.
Prin-
cipal.
Date
In I year .
In 2 years .
In 3 years .
In 4 years .
1.99, 68.31
26.33 74-64
4-6i 39 25
.75 10,00
20.00
40.00
30.00
10 00
66.32
48.31
34-64
9-25
0.00
13-44
12. II
645
1. 68
79-76
71.87
38-32
10.00
20. on
40.00
30.00
10.00
66.32
59-76
3t-^7
8.32
0.00
We thus see that 20.26^ is the "average" of 3, 54^,
133^ and S^^^^s in the sense that, by it, the same pay-
ments will cancel the same debt. It is not identical
with the arithmetical average, which is 19.74^.
§3-
Let ns suppose that the rate of appreciation of one
standard in terms of the other is foreknown to be a^ the
first year, a.^ the second year, a., the third year, and so
on ; also, to be as general as possible, that the rates of
interest in both standards are variable, being in the ap-
preciating standard i^ the first year, i., the second, etc.,
and in the depreciating standard, y^, y^, etc. Let the
final settlement occur in n years. Then, as in § 2, we
may regard the contract as equivalent to a series of one-
year contracts successively renewed in whole or in part,
the difference being only that the terms are all made in
advance. As equation (2) applies to each of these con-
tracts, we have
I +yx =(! + «,) (! + ?■,)
(9)
To obtain an expression for the average rate of inter-
est in either standard, i. <?., z „ (ory J, we require a given
series of payments Z?^, Z>^, . . . Z>„ in the gold standard
369] Appreciation and Interest. 27
(or their equivalent B^, B.^^ . . . B^^ in the silver
standard). The aggregate present value of these
payments, reckoned by the separate rates of interest,
^i^'^2^ . ■ iiorjnJ, . . yjis
l+i, ' (I + i,) ( I + /J ^ ^ (I + Zj (I + tj . . . (I + 4)
(or the corresponding expression in terms of j^'sand/'s).
Now the " average " rate i ^^ must be such that if applied
to the same set of payments it will make the same sum
of present values ; that is, i^ is determined by
1 + 4 ' (1 + 4)- ' (i + 4r
(10)
i + 4^(i + 4)(i + 4)^ ^(i + 4)(i + /j • • (i+?j
and j\^ is determined by the corresponding formula in
^'s and y 's.
This equation has only one real and positive root or
value of i ^. It can readily be obtained by Horner's
Method/ We shall call z^ and /^^ the "actuarial aver-
age" of ?„ ?„ • . z; and of /„ /„ . . /„ re-
spectively.^
' For, h\ substituting for -, the single letter x and for
1 + 4 I + 4>
, etc., the letters x^, .tr„ etc., the equation becomes :
1 + 4
D^x + D^x""-^ ■ ■ +D^x'^ = D^x^-{-D^x^x^+ . ■ +D^x^x^ . . x^.
In the example of I 2, the equation becomes :
20 .ar + 40 ;r^ + 30 .ar^ + ID .ar* = 66 321,
the required root of which is x = .83155,
which, applied to ^^ , gives j\^=^ .2026.
I+7a
* I + 4 reduces to the "geometrical average " of i + 4» i + 4) ^^c. .
when Z?, = Z>, = . • = D.-, = o.
28 American Economic Association. [37°
§5.
We may define tlie average rate of appreciation of one
of the two standards in terms of the other as that rate
which would connect the two average interest rates if
the latter were actual (instead of averages of actual) rates. ^
That is, the average appreciation, a,_^^ is given by the
equation
or a -^iiJZ^? (11)
Thus in the example of §1, the average silver interest
is 20.26^ and gold interest 3^ so that
.2026 — .0^ r„i,
«a= , = ■ 1676,
I + .03
or 16.76^. This average is not identical with the
arithmetical average of o, 50, 10 and 5^s, which would
be 16.25%, ^^*^^ i^ it identical with that rate which if
uniform would result in four years in the same diver-
gence between silver and gold as was produced by the
four successive rates o, 50, 10 and 5/^s; this would be
14.70%. For the statistical purposes of Part II., how-
ever, the latter method is adopted for simplicity and is
doubtless correct within the limit of error.
§ 6.
It may seem that the subject of this chapter can have
no practical application. In Part II we shall see that
this is not the case. A government bond, for instance, is
a promise to pay a specific series of future sums, the
price of the bond is the present value of this series and
^ It may be proved that this definition of a^, satisfies the general
condition of au average, viz., that a^ reduces to a,, a^, etc., when the
latter are all equal, whether z,, i^, etc. {and j\.j\, etc.,) be all equal
or not.
37 1] Appreciatio7i and hiterest. 29
the " interest realized by the investor " as computed by
actuaries is nothins: more nor less than the " averao-e "
rate of interest in the sense above defined. Of course
the investor puts no specific values on the individual
yearly rates of interest of which the "interest realized "
is the average, but that this interest is truly an average
is attested both by the comparative stability of the rate
of interest realized on long time bonds as compared with
the fluctuations of the rate of interest in the short time
money market ( a stability which the rate realized on the
bonds does not possess when near maturity^ ) and by the
fact that interest realized on a very long bond, say 50
years, is often lower than on a 25 years' bond. This is
explainable by the prevailing opinion that interest tends
to fall, so that if the 50 years' investment were in two
successive bonds of 25 years each, the interest realized
in the second would be lower than in the first. The
" actuarial average " of the two is equal to the interest
realized on the 50 years' bond.
' This is abundantly verified by market quotations, as is also the
fact that the interest realized to him who buys a bond and sells it
again in a short time is even more variable than rates on money.
Thus, if in a fortnight ( in which no interest falls due ) the bond ad-
vances y%, the speculator realizes at the rate of about 3% per annum ;
if the rise is %, he realizes over 12%. The investor who holds a bond
along time realizes an interest which is an "average " of the oscillat-
ing rates of those who speculate during the interim.
CHAPTER VI.
ZERO AND NEGATIVE INTEREST.
Having established the truth and generality of the
principle i +/ = ( i + <^) (i + z"), we next inquire what
limits, if any, are imposed on the three magnitudes
y, rt-, i. The foregoing equation seems to require that,
when the appreciation is sufficiently rapid, the rate of
interest in the upward moving standard should be zero
or negative. Thus if a =j\ the equation gives us i= o.
iVgain if « >y then z < o. For instance, if /, the rate
of interest in wheat, is 8 ^ and if gold appreciates rela-
tively to wheat 20^/0 per annum, we have i -J- .08 :=
(i + .20) (i + i) whence i= — .10 ; that is, the rate of
interest in gold would be minus 10 fo I
Now it is clear that negative interest is impossible.
Any possessor of $100 of gold (or its equivalent in goods
which can be sold for gold) would hoard the gold rather
than lend it at a loss. That is, the relation z < o is im-
possible and therefore also « >/ is impossible. Thus
our magnitudes are restricted within certain limits, viz.,
z > o
(12)
or, in words, the rate of interest in a money which can
be hoarded (without trouble, risk or expense) can never
sink below zero and the money itself can never undergo
an expected appreciation (relatively to another standard)
greater than the rate of interest in that standard.
373] Appreciation and Interest. 31
§2.
This last result will not seem mysterious when we re-
flect that the same cause, viz., hoarding, which prevents
the interest from being negative also checks the expected
rate of appreciation. An example will make this clear.
It is a familiar fact that the expected rate of appreciation
of real estate (relatively to money) can never be more
rapid than the rate of interest (in money). If the latter
is 5^, the (money) value of land can never advance
faster than 5 ^ per annum except when that advance is
unforeseen.
The explanation is simple. If it were foreknown that
certain land values would rise 10^, owners would be
able to make twice as much by holding as by selling
and investing the proceeds at 5^. The land would be
hoarded. This decreases the supply and sends up the
price until it is within at least sfooi the expected sell-
ing price one year hence. It thus happens that holding
city lots for speculation comes to be regarded as a regular
investment from which the same return is to be ex-
pected as from investing in a productive enterprise. The
same could be said of wheat, cotton, or other specula-
tion. Hoarding money is but a particular form of
"holding for a rise." In all cases the process tends to
lessen the rise — not to obliterate it but to make it equal
to the rate of interest (in the standard in which the rise
itself is measured).
In the case of appreciating money we saw that, of the
two conditions i~ o and a ^j\ the first was the more ob-
vious, while in the case of appreciating real estate the
second was the more obvious. The reason is that in
both cases we are accustomed to think in terms of
money. We say, " the rate of interest cannot be nega-
32 American Economic Association. [374
tive," " the expected rise of real estate cannot exceed
the rate of interest," but, as we have seen, each of these
statements implies another. It may strike the reader as
a new idea that land speculation presents an actually
existinp- case of zero interest. And yet this is undoiibt-
edlv so, if we take as our standard an acre of speculative
land. The land speculator is " making money " but not
" making land." His 100 acres remains 100 acres. We
could even imagine all loan contracts translated from
" dollars " into " acres " (though still keeping money as
the mcdiitni). K debt of 100 " acres " would be liquid-
ated one year hence by 100 " acres " and interest would
be nil. There is no intrinsic reason why this same zero
interest (for absolutely safe loans) might not sometime
be true of money, and this without implying any change
in the abundance of capital.
§3.
It is important to emphasize the fact that these limits
imposed on the magnitudes i and a come from the possi-
bility of hoarding money without loss. If the money were
a perishable commodity, such as fruit, the limit would be
pushed into the region of negative quantities. One can
imagine a loan based on strawberries or peaches con-
tracted in summer and payable in winter with negative
interest.^ Or, again, we may define a " dollar" as con-
sisting of a constantly increasing number of grains of
gold.^ If the weight doubles yearly, such " dollars"
cannot be hoarded without growing fewer with time,
and if interest was previously 5 ^ it will now be minus
^iVz^oy for he who borrows $100 (2580 grains) to-day
iCf. Bolim-Bawerk, " Positive Theory of Capital," pp. 252, 297.
2 Such a definition for either the gold or silver " pound" is implied
in Professor Foxwell's proposal for a " climbing" ratio.
375] Appreciation a^id Interest. 33
will pay back I52.50 (2709 grains) one year hence.
Again we find a real example by recurring to land
speculation. Since to hold land usually involves paying
taxes upon it, the rate of interest in terms of such
" acres" is often, in actual fact, negative.
§4.
In this connection, an apparent difficulty needs to be
explained. If gold should appreciate up to the maxi-
mum limit so that the interest rate were zero for safe
loans, would not all investment cease ? What object
would a capitalist have in investing when he could gain
as much by hoarding ? Nothing could be more natural
than the fallacy here involved and we ought not to be
surprised on finding it among the arguments of certain
bimetallists. For example, the Free Coinage Conven-
tion at Memphis, Tenn., a year ago, adopted the follow-
ing resolution : " The demonetization of either silver or
gold means a fall in the prices of commodities, a dimi-
nution of the profits of legitimate business, a continuing
increase in the burden of debts, with consequent hard
times, idle labor and idle capital., the increasing value
of money promising a surer rettirn to a hoarded dollar
than to an invested oney
The error here contained is the ancient confusion of
capital and money. It is true that a limited^ amount
of gold would be withdrawn and hoarded, but this
would not check the investment of capital any more
than the similar withdrawal of so much copper. If a
hoarded dollar yields a " sure return," a hoarded dollar^ s
' As in the case of land, the hoarding would reach its limit when it
had raised the value (marginal utility) of present money up to the
present value of future money. Hoarding beyond this point would
bring loss.
3
34 American Economic Association. [.37^
worth of goods as surely bri?tgs loss. The possessors of
stocks of cotton or grain, machinery or ships, the prices
of which are falling, have no disposition to keep them
unemployed. A retail dealer fills his store with carpets
and gives the wholesale dealer his note for three months.
He is said to borrow " money" but he really borrows
carpets. He may pay no (money) interest and yet the
wholesaler gains by the loan. He is saved a loss in the
(money) value of the carpets which he would have in-
curred had he failed to get rid of them. In terms of
carpets he may be making 5^. Similar considerations
apply when the loan is negotiated through a third party,
as a bank, and apply in fact to all forms of loans and
investments. But the case supposed is so highly hypo-
thetical and the error involved has been so often ex-
plained ^ that no further treatment of it seems necessary
here. However turned or twisted and from whatever
point of view examined, lending " money" at no per
cent, may under certain circumstances be a very profita-
ble transaction. It goes without saying that the fore-
going conclusions apply only to " pure" or " net"
interest. That part of market interest representing
risk, and that part representing commissions for transact-
ing the business of lending and borrowing would not
disappear.
^E. g. F. A. Walker, "Money.." (New York, 187S), p. 94.
PART II. FACTS.
CHAPTER VII.
INTRODUCTION.
No study of the relation between appreciation and in-
terest would be complete without verification by facts.
In imaginary illustrations, such as those used in Part I,
it is easy to make calculations agree to the last decimal
place ; but the figures in which we are really interest-
ed must come from actual market quotations. Through
these alone can we test our assumption that foresight in
regard to the appreciation or depreciation of money ac-
tually exists.
At the outset the question arises, how can a merchant
be said to foresee the appreciation of money ? Appreci-
ation is a subtle conception. Few business men have
any clear ideas about it. Economists disagree as to its def-
inition, and statisticians as to its measurement. If you
ask a merchant whether he takes account of appreciation,
he will say he never thinks of it, that he always regards
a dollar as a dollar. Other things may change in terms
of money, but money itself he is accustomed to think
of as the one fixed thing. But though we do ordinarily
regard the value of a dollar as a fixed magnitude, this
does not really prevent our taking account of its changes.
In our daily life we think of the earth as fixed, but we
virtually take account of its rotation whenever we speak
of sunrise or sunset. During a period of inflation the
ordinary man conceives the premium on gold as a rise of
^6 American Economic Association. [378
gold not a fall of money. But if he takes account of
rising wages and rising prices he arrives at the same re-
sults as if he had thought of falling money. We need
not ascribe to the practical man any knowledge of
" absolute " appreciation, but whatever absolute apprecia-
tion is, it is included, though unseparated, in the practical
man's forecast in terms of money of all the economic
elements which concern him — prices of his product,
cost of living, wages of his workmen, and so forth. If
he expects falling prices and rising wages, as is often the
case, he may be said to foresee an appreciation of gold
as defined by the ordinary bimetallist and at the same
time a depreciation as measured by difficulty of attain-
ment. What is more, he takes account of the relative
importance, as affecting himself, of the various changes
which he expects, and not of their relative importance
in the elaborate averages of the statistician, averages
which may emphasize some commodity or some labor
whose fluctuations have absolutely no concern for him.
His effort is not to predict the index numbers of Sauer-
beck or Conrad, but so to foresee his own economic fu-
ture as to make reasonably correct decisions, and in par-
ticular to know what he is about when contracting a loan.
If gold appreciates in such a way or in such a sense that
he expects a shrinking margin of profit, he will be cau-
tious about borrowing unless interest falls ; and this very
unwillingness to borrow, lessening the demand in the
" money market," will bring interest down. Further
explanation of this process is postponed to Chapter X.
Before proceeding to specific statistics, it is important
to emphasize the broad fact that in general, business fore-
sight exists and that the accuracy and power of this fore-
379] Appreciation and Interest. 37
sight is greater today than ever before. It is one of the
distinguishing marks of modern business. Multitudes
of trade journals and investors' reviews have their sole
reason for existence in supplying data on which to base
prediction. Every chance for gain is eagerly watched.
An active and intelligent speculation is constantly going
on which, so far as it does not consist of fictitious
and gambling transactions, performs a well known
and provident function for society. Is it reasonable
to believe that foresight, which is the general rule, has
an exception as applied to falling or rising prices ? Or,
if so, can the academic bimetallist assume himself pos-
sessed of a foresight of which he says the practical man
is incapable ? It is the practical man's business to fore-
see. It is he who first gathers the facts and statistics on
which forecasts must be based. It is he who watches
the trend of past price movements and notes the slight-
est signs of a change. And it is in his trade journals
that we find the first discussions of the probable effect of
gold discoveries or silver legislation on prices and trade.
The theorist can aid in these predictions only by sup-
plying or correcting the principles on which they are
constructed.
CHAPTER VIII.
GOLD AND PAPER.
§1.
General evidence that an expected cliange in the value
of money has an effect on the rate of interest can be ob-
tained from several sources. Municipalities often find
they can sell gold bonds at better terms than currency
or coin bonds. The very desire of lenders to insert a
gold clause in their contracts is strong proof that they
are willing to yield something for it. This was strik-
ingly shown in California^ during the war inflation
period, where for a time, gold contracts could not be en-
forced and in consequence interest rates were very high.
During a period of progressive paper inflation it is also
true that interest is high even when the contract is
drawn on a paper basis. As we shall see at a later stage,
this was partially true during the civil war, though its
effect was not very pronounced owing to the over san-
guine hopes of an early termination of the war and a
return to a specie basis. It was also true during the
currency troubles in the thirties. Raguet wrote : " "In
the six months before the suspension of ^2>7i although
the amount of the currency was greater than it had ever
been before in the United States, yet the scarcity of
money was so great that it commanded from i^o to 3 ^
per month." It would be unsafe to found much infer-
ence on these facts. Their significance may be partly
^ Bernard Moses, " Legal Tender Notes in California," Quarterly
Journal of Economics, October, 1892, p. 15.
-" Currency and Banking," (1839), p. 139; alsoSumner, " History; of
Banking," (1896), p. 264.
38 1]
Appreciation a7id Interest.
39
or wholly different. But they raise a presumption in
favor of the theory here advanced and against the theory
that the rate of interest is lowered by inflation of the
currency.
A definite test must be sought where two standards
are simultaneously used. An excellent case of this kind
is supplied by two kinds of United States bonds, one
payable in coin and the other in currency. From the
prices which these bonds fetch in the market it is pos-
sible to calculate the interest realized to the investor.
The currency bonds are known as currency sixes and
mature in 1898 and 1899. The coin bonds selected for
comparison are the 4^5 of 1907. The following table
gives the rates of interest realized in the two standards
together with the premium on gold.
RATES OF INTEREST REALIZED FROM
DATES MENTIONED
TO MATURITy.i
Price of
Coin.
Currency.
Coin.
Currency.
6.4
Gold.
Jan.,
1870 .
5-4
119. 9
Jan..
1879 • •
1 3-7
4-5
July.
1870 .
5-8
5-1
112. 2
Jan.,
1880 .
i 3-8
4.0
Jan ,
187T .
6.0
5-3
I TO 8
Jan.,
1 881
• 3-3
3-4
July,
1871 .
5-8
50
113. 2
Jan.,
1882
1 3-0
3-5
Jan.,
1872 .
5-3
4-9
109.5
Jan. ,
1SS3
2.9
3-3
July.
1872 .
56
5.0
113-9
Jan.,
T884
\ 2.6
2.9
Jan.,
1873 •
5-7
5-1
III. 9
May,
1SS5
1 ^-7
2.7
July,
1S73 •
5-4
50
"5-3
Jan.,
t886
1 2.6
2.6
Jan.,
1874 •
5-0
5-0
110.3
Jan.,
1887
2.3
2.6
July,
1874 .
50
4-9
T10.7
Mar.
t888
2.3
29
Jan.,
1875 •
5-1
47
112. 6
Jan.,
1889
2.2
2.6
July,
1875 •
51
4-4
1 17.0
May,
1S90
2.T
2.6
Jan.,
1876 .
4-7
4.4
112. 9
July,
189T
2.4
3-0
July,
1876 .
4-5
4.2
112.3
Jan.,
1892
i '-^
3-1
Jan.,
1S77 .
45
4.4
107.0
Mar.
1S93
i 2.8
3-1
July,
1877 .
4.4
4-3
105.4
Nov.
, 1894
2.7
3-5
Jan.,
1878
50
4.6
102.8
Aug.
,1895
2.8
3-6
July,
1878 .
3.9
4.4
TOO. 7
Aug.
, 1896
3.2
4-3
^This table has been obtained by the aid of the usual brokers' bond
tables. In the case of currency bcir.ds, it was only necessary to deduct
accrued interest (if any) from the quoted price and look in the table
for the interest which corresponds to the price so found and the num-
40 American Economic Association. ^ [382
Several points in this table deserve notice. The quo-
tations for 1894, '95, '96 show a considerably higher rate
of interest in the currency standard than in the coin stand-
ard as well as a higher rate in both standards than in
previous years. The difference is between 2.7^ and
3.5^ in 1894, and between 3.2^ and 4.3^ in 1896.
Both the increase and the wedging apart of the two rates
are explainable as effects of the free silver proposal and
its incorporation (July 1896) in the platform of the
Democratic party. A free silver law v^^ould certainly re-
duce the value of returns from currency bonds and possi-
bly also of those from coin bonds. If the mere dread of
inflation has this effect, it might be supposed that, dur-
ing the period of actual inflation, the discrimination in
favor of coin bonds would be even greater. But we find
the exact opposite to be true. In 1870 the investor
made 6.4^ in gold but was willing to accept a return of
only 5.4^ in currency. This fact becomes intelligible
in the light of the theory which has been explained. It
meant the hope of resumption. Just because paper was
so depreciated there was a prospect of a great rise in its
value. It was not until 1878 when the prospect of a
further rise disappeared that the relative position of the
two rates of interest was reversed. After resumption in
1879 the two remained very nearly equal for several
years until recent fears of inflation again produced a
divergence.
ber of years to maturity. In the case of gold bonds, since the quota-
tions are given in currency, it is necessary to divide the quoted price
by the price of gold in order to obtain their price in gold {i. e.,
"coin") and then proceed as above indicated. The quotations of
prices of bonds and gold are the "opening" prices for the months
named and are taken from the Financial Reviezv, 1895, the Commer-
cial and Fitiancial Chronicle, the (New York) Bankers' Magazine
and the Bankers' Almanac. After 1SS4, January quotations were not
always available.
383] AppreciatioJi and Interest. 41
§3-
We have found so far that the facts agree with the
theory previously laid down. But it is necessary further
to inquire how close is this agreement. For this pur-
pose, the figures just given are of little value. They
represent the rates of interest realized for the periods be-
tween the dates named and the times at which the bonds
mature. These periods are not the same for the two
bonds. As has been explained such a rate of interest is
a sort of average of the rates of interest for the individual
years of the periods in question. Thus, in the foregoing
table, the rate of interest in currency opposite January,
1870, is 5.4^. This is the rate realized between 1870 and
1899. It is a sort of average of, say, the rate realized be-
tween 1870 and 1879 and between 1879 and 1899. As
we shall see the former was 6.3^ and the latter, 4-5/^.
It is clear that we must seek the rates of interest in
the two standards for the same periods. In the follow-
ing table the periods selected terminate on Jan. i, 1879,
the date of resumption of specie payments. We may
say, to fix our ideas, that the figures represent the rate of
interest realized to investors who buy the bonds at the
dates mentioned and sell them on January i, 1879 ; but
it is obviously unnecessary to consider the bonds as ac-
tually either bought or sold, but only as owned. This
is no nevv^ use of terms. Business men reckon securities
in their assets at their market prices and if these prices
rise or fall they count themselves as gainers or losers.
This gain (or loss) added to the annual interest receipts
and properly distributed over the time considered gives
the rate of interest realized.
42
American Economic Association.
[3S4
RATES OF INTEREST REALIZED FROM DATES MENTIONED TO JAN-
UARY I, 1879, (Date of Resumption').
Coin.
Currency.
Appreciation of Currency in Gold.
Expected.
Actual.
j
i
a
January, 1S70. . . q.i
6.3
.8
2.1
July, 1S70 . .
6.2
5-7
•5
1.4
January, 1871 .
6.7
63
•4
1-3
July, 1S71
6.4
5-7
• 7
1.8
January, 1S72 .
5-9
5-7
.2
1-3
July, 1S72 .
6.2
5-7
•5
2 1
January, 1873 •
6.5
62
.3
2.0
July. i'S73 • ■
6.2
6.0
.2
2.8
January, 1S74.
5.6
6 T
—.5
2.T
July. 1874 . .
5-7
5-8
2.4
Fanuary, 1875 •
6.0
5-4
!6
3-1
July, 1875 • .
6.1
4.2
1.8
4-9
January, 1876.
5-4
41
1.2
43
July, 1876 . .
5-2
2.4
2.7
4.9
January, 1877 .
5-5
4.0
1.4
3-5
July, 1 87 7 . .
5.7
3-1
2.5
3.6
January, 1878.
8.2
6.0
2, 1
2.8
July, 1878 . .
4.8
2.6
2,1
1.4
' Since the figures in this table represent the rales of interest which
will render the " present value," at the date of purchase, of all the
future benefits to January, 1879, equal to the purchase price, they can
be calculated by Horuer's method as indicated in Chapter V. But the
method which has been adopted is less laborious, as it ena1)les us to
use the bond tallies. It can best be explained by an example. The
opening price, January, 1870, of currency 6's was 109)^, and January,
1879, ^^9/i, which require no correction for accrued interest. Our
problem is, if a man spends ^109"/^ in 1870 and receives |ii9>< in
1879 with $6 per annum (semi-annually) in the meantime, what rate
of interest does he realize? Now it is clear that the answer is the
same if all the benefits and sacrifices involyed are doubled or halved
or increased or decreased in an}' common ratio. Let us then divide
them all by i.icjyi- Then I91.3 would be paid in 1870 for |;ioo due in
1879, and ^5.02 per annum in the meantime. That is, the interest
realized is exactly as if the bond were a 5.02% bond maturing in 1879
and bought at 91.3 in 1870. This can readily be obtained from the
bond tables by interpolating between the figures for a 5% and a 5)4%
bond purchased at 91.3 and having 9 years to run. For a 5% bond
we obtain 6.28%, and for a 5}4% bond, 6.81%. Hence for a 5.02%
bond the result is 6,30%, or 6.3%, The third column gives what may
be called the expected rate of appreciation of currency in terms of
gold, that is, that rate of appreciation which would have made the
385] Appreciation and Intej^est. 43
From this table we see that the interests realized for
the period, January, 1870 to January, 1879, were, in coin,
7.1^, and in currency, 6.3%, which, according to the
formula i + 7 = ( i + z ) ( i + <« ), gives a rate of appre-
ciation of .8%. This may be called the " expected ap-
preciation ". The actual rate of appreciation was 2.1%.
That is, the estimated appreciation was about two-fifths
of the appreciation as it really turned out. Thus those
who held currency sixes had the better investment. In
fact it is w^ell known that many speculators grew rich by
exchanging gold bonds for currency bonds at this time.
The table shows the same misjudgment in July, 1870,
January, 1871, and July, 1871. From then to July,
1874, the outlook for resumption grew gloomy, due no
doubt to the strong greenback sentiment. The inflation
bill of 1874 actually produced a prospect of negative
appreciation, i, e.^ depreciation. This bill was vetoed by
President Grant, and in December of that year the bill
for resumption was passed by the Senate. Accordingly
January, 1875, opened with a more hopeful estimate.
The bill became law on the 14th of January and there
was an immediate rise in the " expected " appreciation
which, from then on, averaged 2%. But during the
same period the actual appreciation from the dates named
two interest rates equally profitable. It is obtained from the formula
I +y= (i -I- ?■) (i + «)• The last column gives the actual rate of ap-
preciation between the dates mentioned and January i, 1879. This
is calculated from the quoted prices of gold. Thus the opening price
of gold January, 1870, was 119.9, and January, 1879, ^oo- Hence
currency appreciated in nine years in the ratio 100 to 119.9, which is
at the race of 2.1% per annum. If the appreciation proceeded uni-
formly this method would be strictly correct. As it is, a more elabo-
rate method would be required, in accordance with the principles ex-
plained in Chapter V, to take account fully of the fluctuations of the
annual appreciation. But for our present purposes, and for results
worked out to but one decimal place, the simpler method here
adopted is sufficiently correct.
44 American Econoviic Association. [386
to January, 1S79, averaged 3.6%, so that even after the
government promised resumption, investors and specula-
tors did not put implicit confidence in that promise, the
"expected" appreciation being only a little more than
half the actual appreciation. This corresponds to the
well known fact that the resumption act was then looked
upon as a political manoeuvre, likely to be repealed.
It should be observed that the method employed to
determine the rate of interest realized is open to oiie
danger. It correctly represents the rate of interest act-
ually realized between tw^o dates, but, unless the later of
the two dates is maturity, it does not necessarily repre-
sent the rate of interest expected at the first date. The
investor could not know in January, 1870, what the price
of bonds would be in January, 1879, unless the bonds
matured at that time. To compare, in 1870, the relative
advantages of coin and currency bonds for the period
1870-79, a forecast was necessary, not only of the rela-
tion of currency to gold, but also of the prices of the two
bonds in 1879. These prices in turn depend on a new
forecast made in 1879. It follows that a mistake in this
forecast of 1879 ^^^ embodied in the prices of that year
wall affect the rate of interest realized between 1870 and
1879 in the same manner as a mistake of the opposite
kind in the forecast of 1870.
But in most cases the method given is sufficiently
exact. For, although in 1870 it would have been im-
possible to predict exactly the prices of the two bonds in
1879, yet it can usually be depended upon that any great
change in price is apt to affect both alike (provided they
have approximately the same time to run) and thus
387] Appreciation and Interest.
45
eliminates itself for the most part in the comparison.
For this reason it is clearly better to take bonds whose
dates of maturity approximately correspond, in order
that any abnormal influence in 1879 may affect both
alike, than to take, for instance, currency sixes of 1899
and coin bonds of 1881.
48 American Economic Association. [390
From this table it will be seen that the rates realized
to investors in bonds of the two standards differed but
slightly until 1875, when the fall of Indian exchange
began. The average difference before 1875 was .2^
while the average difference since 1875 has been .7^,
or more than three times as much.
From 1884 exchange fell much more rapidly than be-
fore, and the difference in the two rates of interest rose
accordingly, amounting in one year to i.i^. Since
the two bonds were issued hy the same government,
possess the same degree of security, are quoted side by
side in the same market and are in fact similar in all
important respects except in the standard in which the}-
are expressed, the results afford substantial proof that
the fall of exchange (after it once began) was discounted
in advance. Of course investors did not form perfectly
definite estimates of the future fall, but the fear of a fall
predominated in varying degrees over the hope of a rise.
The year 1890 was one of great disturbance in ex-
changes, the average for the first six months being 17.6
and for the last six months 19.3. The gold price of
the silver bonds rose from an average for the first six
months of 73.8 to 83.5 for the last six months, but the
rise in their silver price was only from 100.6 to 103.7,
showing that the increase of confidence in the " future
of silver" was not great and in fact only reduced the
disparity in the interest from i.o to .8^.
This great rise in exchange and the slight revival in
silver securities occurred simultaneously with the pas-
sage of the Sherman act of July, 1890, by which the
United States was to purchase four and a half million
ounces of silver per month. There can be little doubt
that the disturbance was due in some measure to the
operation or expected operation of that law.
39 1] Appreciation and Interest. 49
This is not the only case in which the relative prices of
rupee paper and gold bonds were probably affected by po-
litical action. The smallest difference (since 1874) in
the tw^o rates of interest occurs in 1878, which was the year
of the Bland act and the first international monetary
conference.
After the closure of the Indian mints on June 26, 1893,
exchange rose from 14.7 to 15.9, the gold price of rupee
paper from 62 to 70 and consequently its rupee price
from 101.2 to 105.7.
§ 2.
The preceding comparisons serve to establish the in-
fluence of the divergence between the standards on the
rates of interest, but afford no measure of that influence.
The rates of interest which have been deduced for gold
bonds were the rates realized if the bonds were held to
maturity. The rupee bond had no fixed date of matur-
ity and had to be treated as a perpetual annuity, although
it differed from such an annuity in being terminable by
the government at par on three months' notice.
In order to measure the extent to which the fall of silr
ver was allowed for by investors, it is necessary to exam-
ine the rates realized during specified periods. The fol-
lowing table gives the rates realized between the first
five and the last five years of the period of falling ex-
change.
50
American Economic Associatioii.
[392
RATES OF INTEREST REALIZED ON INDIA BONDS FOR PERIODS
SPECIFIED.!
Silver.
.
J
Gold.
i
Appreciation of Gold in
Silver.
Estimated.
a
Actual.
1875-91 ....
1876-92 ....
1877-93 ....
1878-94 ....
1879-95 ....
4.1
4.3
4-5
4.6
4.8
3-5
3-6
3-6
3.8
3-9
.6
.7
•9
.8
•9
1.6
1.8
2.1
2.6
2.4
Average ....
4-5
3-7
.8
2.1
The average estimated appreciation for the periods
taken is .8%, which is slightly more than one third of
the average actual appreciation, 2.1%. Perhaps to ob-
tain the net estimate of investors as to the fall of ex-
change we ought to deduct from the .8% another .\^'/o due
to the trouble and expense of obtaining English money
for Indian exchange, for it will be remembered that even
before the fall of exchange began, the rates yielded to
investors differed by .2%.^ We thus obtain ,7% as the
extent to which, on the average, investors protected
themselves against the fall in silver during the period
' The methods by which the first columu is computed are the same
as those explained in the preceding chapter, account being taken of
the fact that the price quotations for rupee paper are not "flat," so that
no corrections for accrued interest need be applied. For computing
the second column a more laborious method was necessary, due to the
fact that the quotations are not continuous for the same bond. The
earlier ones are for a 4 % bond and the later for a 3 % bond. The
buyer of a 4 % bond is regarded as converting it into the 3 % at the
current price in 1888, the date of maturity of the earlier bond. As no
bond tables apply to such conversions, tables of present values were
used and that rate was found by trial (and interpolation) which would
make the present value of all benefits equal to the purchase price.
^This probably included besides the brokerage and trouble of ob-
taining and selling " interest bills ", the risks even at those early
dates of a falling or fluctuating exchange.
393] Appreciation and hiterest. 51
named. The remaining fall, 1.4%, implies a rela-
ative loss to the holders of rupee paper and a gain
to the holders of gold bonds. Had the business
world fully foreseen the fall of Indian exchange, rupee
paper would have been cheaper or gold bonds dearer
than they actually were, or both. The rates of interest
realized in the two standards during the periods men-
tioned would have been spread apart ( at most ) i ^/^ ^
further.
§3.
The question arises at this point, how is this 1)4 fo to
be distributed? Did investors overestimate silver or
underestimate gold most ? There is nothing in the fore-
going investigation to decide this vexed question. Our
quantitative result is purely a differential one. But
other sorts of evidence point strongly to the conclusion
that the major part of the miscalculation was on the sil-
ver side. So far as " demonetization " is concerned, the
effect on silver must have been, according to any reason-
able view, greater than the effect on gold, and in conse-
quence any unforeseen part of these effects would be
probably greater in the case of silver than in the case of
gold. So far as production is concerned, the disturb-
ance in silver was far greater than that in gold either
when reckoned absolutely or in proportion to the total
masses whose values would be affected. Finally, since
the break-down of bimetallism in 1873-4, the world-wide
agitation to " rehabilitate silver " has held out a delusive
hope which must have acted to give the silver bonds a
higher price than they " were worth." The strength of
this agitation need scarcely be dwelt on here. It found
expression in many bills in Congress which were never
passed and in two which were passed, in numerous pro-
50
American Economic Association.
[39-
RATES OF INTEREST REALIZED ON INDIA BONDS FOR PERIODS
SPECIFIED. 1
Silver.
Gold.
Appreciation of Gold in
Silver.
Estimated.
Actual.
J
z
a
1875-91 ....
1876-92 ....
1877-93 • . . .
4.1
4.3
4-5
3-5
3-6
3.6
.6
• 7
•9
1.6
1.8
2.1
IS78-94 ....
4.6
3.8
.8
2.6
1879-95 ....
4.8
3-9
•9
2.4
Average ....
4-5
3-7
.8
2.1
The average estimate4 appreciation for the periods
taken is .8%, which is slightly more than one third of
the average actual appreciation, 2.1%. Perhaps to ob-
tain the net estimate of investors as to the fall of ex-
change we ought to deduct from the .8% another , i % due
to the trouble and expense of obtaining English money
for Indian exchange, for it will be remembered that even
before the fall of exchange began, the rates yielded to
investors differed by .2%.^ We thus obtain .7% as the
extent to which, on the average, investors protected
themselves against the fall in silver during the period
^ The methods by which the first column is computed are the same
as those explained in the preceding chapter, account being taken of
the fact that the price quotations for rupee paper are not "flat," so that
no corrections for accrued interest need be applied. For computing
the second column a more laborious method was necessary, due to the
fact that the quotations are not continuous for the same bond. The
earlier ones are for a 4 % bond and the later for a 3 % bond. The
buyer of a 4 % bond is regarded as converting it into the 3 % at the
current price in j8S8, the date of maturity of the earlier bond. As no
bond tables apply to such conversions, tables of present values were
used and that rate was found b}' trial (and interpolation) which would
make the present value of all benefits equal to the purchase price.
^This probably included besides the brokerage and trouble of ob-
taining and selling " interest bills ", the risks even at those early
dates of a falling or fluctuating exchange.
393] Appreciation and Interest. 51
named. The remaining fall, 1.4%, implies a rela-
ative loss to the holders of rupee paper and a gain
to the holders of gold bonds. Had the business
world fully foreseen the fall of Indian exchange, rupee
paper would have been cheaper or gold bonds dearer
than they actually were, or both. The rates of interest
realized in the two standards during the periods men-
tioned would have been spread apart ( at most ) i ^^ ^
further.
§3-
The question arises at this point, how is this i}4 fo to
be distributed? Did investors overestimate silver or
underestimate gold most ? There is nothing in the fore-
going investigation to decide this vexed question. Our
quantitative result is purely a differential one. But
other sorts of evidence point ^t^ongly to the conclusion
that the major part of the miscalculation was on the sil-
ver side. So far as " demonetization " is concerned, the
effect on silver must have been, according to any reason-
able view, greater than the effect on gold, and in conse-
quence any unforeseen part of these effects would be
probably greater in the case of silver than in the case of
gold. So far as production is concerned, the disturb-
ance in silver was far greater than that in gold either
when reckoned absolutely or in proportion to the total
masses whose values would be affected. Finally, since
the break-down of bimetallism in 1873-4, the world-wide
agitation to " rehabilitate silver " has held out a delusive
hope which must have acted to give the silver bonds a
higher price than they " were worth." The strength of
this agitation need scarcely be dwelt on here. It found
expression in many bills in Congress which were never
passed and in two which were passed, in numerous pro-
52 American Economic Association. [394
posals in Germany, in silver commissions there and in
England, and in three international conferences. If any
further evidence is needed that this agitation contrib-
uted to mislead investors as to the future of silver, it
can be found by examining the discussions and mistaken
prophecies on silver, contributed to the Economist and
other trade journals. It would seem extremely improb-
able that these hopes for the " rehabilitation of silver "
have acted to depress the price of gold bonds rather than
to raise the price of silver bonds.
For these reasons it seems likely that, of the lyi'fo
relative gain or loss, not more than half represents an
unexpected gain on the gold bonds. That is, the inter-
est realized on the gold bonds, if higher than it should
be, was not higher by more than Y^'fc If this be true
of one gold investment it was undoubtedly true of all
gold investments and of the whole money market in
London. This affords therefore, a probable upper limit
to the debtor's loss in England for contracts made since
1874. But even if the miscalculation was twice as great
for gold as for silver, the upper limit becomes only i ^.
Our result therefore, is that the average debtor's loss
in London for contracts made since the fall of silver be-
gan, was probably less than y^ ^ and almost certainly
less than i ^ per annum. In Chapter X we shall at-
tempt to find a lower limit.
A great deal has been written on the loss incurred by
India in paying her annual interest to England in gold,
but little is said of the interest paid at home in silver. Of
India's national debt, about ^100,000,000 are in gold
and Rx 100,000,000 in rupees. This rupee debt was
395] Appreciation and Interest. 53
almost all in force twenty years ago and was then equiva-
lent to ^100,000,000, but today it is worth only ^60,-
000,000. The difference may mean an added burden of
gold debt, but it may also mean a lessened burden of
silver debt and it is by no means impossible that, so far
as national indebtedness is concerned, India is better off
than she would, have been if a bimetallic tie between
silver and gold had been maintained.
In this connection it may be worth while to point out
a curious oversight in Mr. Elijah Helm's recent book.^
In Chapter XVI he proposes the conversion of the 4^
rupee debt into a 3^ gold debt and, assuming very
plausibly that the gold bonds could be sold for 99, shows
that so long as exchange remained at its present level,
there would be an annual saving of interest oi Rs
160,000. This is correct enough, but he next attempts
to show that if exchange should gradually fall there
would continue to be a saving until it should sink to
ioj4d. This is entirely erroneous. It takes account only
of the annual interest and not of the deferred principal
which if in gold, grows progressively onerous in terms
of silver. It is odd that a bimetallist who portrays so
vividly the evils to the debtor from an appreciating gold
principal should have found himself in the position of
deliberately advising a debtor to adopt that standard to
lessen his burden of interest. In the same year that
Mr. Helm's book was written, the Indian Government
converted its 4^ rupee debt, not into gold, but into
another rupee debt at S}4 fo.
1 "The Joint Standard," (London and New York, 1894.)
CHAPTER X.
MONEY AND COMMODITIES.
§1.
In attempting to apply our theory to periods of rising
and falling prices, we are met by the difficulty that
comparison can only be made between successive periods.
We can learn what the rate of interest has been since
1873, ^^^ "^^ cannot know what it would have been if
bimetallism had been extended or if the world's cur-
rency had been so expanded as to have prevented the
fall of prices. Without this missing term of compari-
son, it is difficult to measure the influence of the pro-
gressive scarcity of gold, if such there has been, upon
the rate of interest. It does not answer the purpose
merely to compare the rates of interest before and after
1873. No two periods are so alike industrially that we
can say they differ only in the state of the monetary
standard. Other influences innumerable affect the
" value of money" on the money market. Individual
quotations at different times on the same market vary
from one half of one per cent, to fifty per cent, while
yearly averages vary from one to seven per cent. We
can never wholly eliminate all causes but one, and even
partial elimination is possible only by taking averages
for periods of several years each. In spite of these diffi-
culties however, certain general conclusions can be
established.
§2.
Our main problem is not concerned with high and
low prices but with rising or falling prices. But we
397]
Appreciation and Interest.
55
note in passing an important generalization in regard to
price levels and the rate of interest. Shall we associate
high interest with high prices or with low prices ? To
answer this question the following table is constructed.
Two rates of interest are given for each decade. The
MARKET RATES OF INTEREST IX RELATION TO HIGH
AND LOW PRICES.i
1824 to
: 1831
; incl.
1832 to 1842 to
1841 1851
incl. incl.
1852 to
I86I
incL
1862 to
1871
incl.
1872 to
1881
incl.
1882 to
1891
incl.
London, High prices
" Low prices .
13.8
; T, 2
4.4 3-6
3.2 2.6
5-4
3-0
5-1
2.6
3-7
2.5
30
2.5
New York, High prices . .
" Low prices ....
9-1
91
7.4
6.7
7.0
5-1
5-3
5.1
Berlin, High prices
" Low prices .
4.6
3-4
3-7
3-2
3-3
2.7
Paris, High prices . . .
" Low prices ....
i
4.1
2.4
2.6
2.6
^ Calcutta, High prices
" Low prices .
6,2
5-6
5-4
6.2
' Tokyo, High prices . .
" Low prices ....
■
12.3
12.0
lO.I
10. 1
* Shanghai, High prices
" Low prices .
' i
; 6.0
. . ; . . ! . . 1 . .
i 5-7
^ This table is constructed from the data given in the Appendix.
For New York, the rates for the first decade are averaged from the
column in the Appendix headed "60 days," and are not to be com-
pared with those for the remaining decades, which are averaged from
the column headed " Prime two name 60 days." The index numbers
of prices which have been employed are those of Jevons (1S24-51)
and Sauerbeck (1S52-91) for England, Soetbeer and Heinz for Ger-
many, the Aldrich Senate report for the United States and France,
and the Japanese report for India, Japan and China. (See Appendix,
\ 3). The table ends in 1S91 because there are no index numbers for
the United States since that year.
2 For Calcutta the rate for the bank of Bengal is employed, no
"market" rate being available. The first column is for 1873-81 in-
stead of 1S72-81, for the reason that no index number for 1872 is
available.
* For Tokyo the first column is for 1S73-81 for the same reason.
* For Shanghai the period is 1S85-93 instead of 1S82-91, for the rea-
son that the available rates begin in 1885 and the index numbers end
in 1893.
56 American Economic Associatio7i. [398
first, opposite " high prices," is the average rate for
those years of the decade whose price levels, as shown
by an index number, were above the average price level
for the whole decade ; the second is the average rate for
the years whose prices were below the general average.
Of the 21 comparisons contained in this table, 17 show
higher rates for high-price years than for low-price
years, one shows the opposite condition and three show
equal rates in the two cases. As the table covers 68
years for London, 40 for New York, 30 for Berlin, 20
for Paris, 19 each for Calcutta and Tokyo, and 9 for
Shanghai, or 205 years in the aggregate, the result
may be accepted with great confidence that high and
low prices are usually associated with high and low
interest respectively.
There are two probable reasons for this connection.
One is that high general prices usually mean scarcity of
capital rather than abundance of money, while low prices
generally mean abundance of capital, not scarcity of
money. This corresponds to the observations of Jevons
on the relation of the rate of discount to the price of
wheat ; ^ the other reason is connected with periods of
speculation and depression and will be discussed in § 12.
§3.
The relation of high or low |)rices to the rate of inter-
est must not be confused with the relation of rising or
falling prices to the rate of interest ", to which vv e now
turn.
^ "Investigations in Currency and Finance," (1884), p. XIV.
^ de Haas appears to have fallen into this confusion both in his crit-
icism of Jevons and in his treatment of statistics. See "A third
element in the rate of interest," Journal of the Royal Statistical
Society, March, 1889.
399] Appreciation and Interest. 57
It was predicted by Mr. Gibbs/ formerly a director of
the Bank of England, and by other eminent bimetallists
that the progressive scarcity of gold would raise the rate
of interest. Such a scarcity makes a stringency in the
money market, and the banks, each struggling to attract
reserves from the others, will raise their rates. This
prophecy, however, has not been fulfilled. Scarcely had
Mr. Gibbs made his prediction when the rate fell enor-
mously. Some monometallists have argued from this fact
that there has been no appreciation of gold ^. But the
theory that appreciation raises interest has been confi-
dently afiirmed on both sides and has even received the
stamp of approval of Mr. Giffen.^ It is, however, utterly
' "The Bimetallic Controversy," (London, 18S6), pp. 19, 231, 245-8-9,
373-
2 Report of the Gold and Silver Commission, (1888), p. 120; also
Professor Laughlin in Quarterly Journal of Economics, Vol. i., p. 344.
3 " Essays in Finance," (2d series, 1886), p. 70. " The years oi fall-
ing prices and rising prices also correspond as a rule with those years
in which high rates and low reserves, and low rates and high reserves
are combined." This (so far as prices and interest are concerned) is
not only the exact opposite of the truth but it is flatly contradicted by
the few figures which Mr. Giflfen himself brings forward. Of these
he says : " . . in years like 1865 and 1866 with which the Table
begins, there is an obvious connection between the low reserve and
high rate of discount of those years and the high Index No., leading
in the following [!] years 1867-71 to a simultaneous fall in the Index
No. and the rates of discount . . " He adds : " . . the low
prices rather succeed the high discount rates than exactly correspond
. . " Coming to the recent period of gold contraction, he says :
" Turning to the rate of discount, we find the facts once more in cor-
respondence. What we find first is a striking disturbance of the
money market at the maximum period of high prices, 1871-73 [a pe-
riod of rising prices and high interest], when the contraction of gold
begins." Of the period 1875-79 (falling prices and low interest), he
writes: "With a minimum average monthly rate of 2 per cent in
each year, the following maximum monthly rates were nevertheless
touched, viz" : [4^, 4f, 4f, sf, 4^ %s]. "In the present year (1885)
when with dull trade and low prices the reserve should be full and
discount rates low, we find that with a minimum of 2 per cent, there
is again to be a comparatively high maximum (4 %) within the year."
58 American Ecoyiornic Associatio7i. [400
at variance with facts. Tliat an abnormally high or low
bank reserve is correlated with low and high interest is
abnndantly justified in theory and verified in practice.'
But the normal bank reserve itself shrinks with a
shrinkage of gold and in consequence the inference that a
contraction of the general gold supply will raise interest
is fallacious.^
When prices are rising or falling, money is depreciat-
ing or appreciating relatively to commodities. Our
theory would therefore require high or low interest ac-
cording as prices are rising or falling, provided we as-
sume that the rate of interest in the commodity stand-
ard should not vary. This assumption would be thor-
oughly justified only in case the two periods were eco-
nomically alike in all respects except in the expansion
or contraction of credit and currency. In the following
"To sum up — what I have to say of the recent discount rates is that
while there has been an undoubted fall in recent years, corresponding
to the abundance of capital, yet the market has been fevered by the
demands on the reserve . . " "The monetary history of recent
years has accordingly been very like what was to be expected on the
theory above set forth, assuming a contraction of gold to have oc-
curred, . . finally the money market has been irritable and fever-
ish in a remarkable manner during the period of contraction." Thus,
beginning with a statement that years of falling and rising prices cor-
respond to years of high and low interest, Mr. Giffen cites facts which
show that the opposite is true, but proceeds complacently to compare
the rates of periods of rising (or falling) prices with the prices of the
succeeding period of falling (or rising) prices. As the period of fall-
ing prices in which he writes is unfinished, he can onl}- say of it that
the "money market has been irritable and feverish in a remarkable
manner." Another monometallist, Clarmont Daniell, objects to bi-
metallism for India on the ground that it would deplete India of silver
and raise the rate of interest. ( "The Bimetallic Controversy," p. 257).
On this point see \ 5.
^See, ^. ^., Giffen's "Essays," ibid., or the diagrams in Clare's
" Money-Market Primer," L,ondon, 1891 ; also F. M. Taylor, "Do we
want an Elastic Currency," Political Science Quarterly, March, 1S96,
pp. 133-157-
^ See, however, § 12, note.
40i]
Appreciation and Interest.
59
table for London the periods are selected to correspond
with the main movements of prices. Thus the period
1826-29 was a period of falling prices so that money ap-
preciated in terms of commodities at the average rate of
\.2fo per annum. This is indicated in the third column
by the figure +4.2. In the period 1836-39 prices rose
so that money fell at the rate of 2.3^ per annum, indi-
cated by — 2.3.
I^ONDON RATES OF INTEREST IN REIyATlON TO RISING
AND FAI,I,ING PRICES.i
Appreciation of
virtual Interest
Bank.
Market.
i
Money in
Commodities,
a
m
Commodities.
(Market.)
J
1826 — 29 • •
4.4
3-5
4-4.2
7.8
1830—35
4.0
3-2
0.0
3-2
1836—39
4-7
4.2
—2.3
1.8
1840—44
4.2
3-5
+5.9
9.6
1845—47
3-7
4.2
— 3-0
I.I
1848—52
2.9
2-5
+ 1.2
37
1853—57
4.1
5-3
—2.4
2.8
1858—64
4.4
4.2
— 3-0
I.I
1865—70
3-8
3.6
+ 1.1
4-7
1871—73
3-9
3-7
—6.2
—2.7
1874—79
3.2
2.7
-f4-3
7-1
1880—87
3-3
2.6
+3-8
6.5
1888—90
3-8
2.9
—1.4
1-5
1891—95
2.6
1.6
+3.8
5-5
Mean Variation,
•5
■ 7
2.6
^ This table is constructed from the data in the Appendix. The
third column is based on index numbers, (Jevons' for 1826-52, and
Sauerbeck's for the remaining years). The index numbers for two
dates, as 1826 and 1829, being given, their inverse ratio gives the rela-
tive value of money (in commodities), at those two dates. From these
it is easy to calculate the average annual change in its value. Theo-
retically, since the loans here included run usually, perhaps 30 to 90
days, the quotations averaged should begin at the first of the two dates,
and cease, say, 60 days before the second. But the index numbers are
not always for definite points of time, nor can the interest quotations
be subjected to such minute corrections without an immense expendi-
ture of labor. Hence, the method adopted has been to average the
rates for all the years of a period, e.g., for the four years, 1S26-29,
while the "appreciation" is reckoned between those dates, and
thus is an average for only three years. If the index numbers repre-
6o American Economic Association. [402
If this table be exaiiiiiied in successive periods, it will
be found, in eleven out of thirteen sequences for bank
rates and in ten out of thirteen for market rates, that in-
terest is high or low according to the degree in which
prices are rising or falling. Attention is called particu-
larly to the period 1S53-57 during which prices rose
very fast simultaneously with and presumably because
of the great gold production. The market rate of in-
terest averaged 5.3/^ which was far higher, not only
than in any subsequent, but also than in any previous
period, although it can scarcely be supposed that capital
was less abundant This fact has been commented upon
by various writers, ^ and is usually attributed to trade ac-
tivity and speculation. Such a reason, however, is not
really explanatory unless the reason for the speculation
is also given.
The theory here offerred, that the high rate represent-
ed an effort to offset the depreciation of money, not only
affords a complete explanation but in connection with
another fact soon to be noted, explains the trade activ-
ity also.
§4-
The following table for Berlin displays the same con-
nection between price movements and interest.
sent the price levels at the middle of 1826 and of 1829, then the average
interest rates ought in theory to include only the last six months of
1826, and the first four months of 1829. But it seems better to include
too much at both ends, than to omit the averages for 1826 and 1829
altogether, for the reason that an average is the more valuable the
greater the number of terms included. The method adopted also
seems better than omitting either otie of the extreme years, partly for
the reason just given, and partly because both years usually belong
to the same economic movement.
^ E.g., Sir Louis Mallet. Note to Report of Gold and Silver Com-
mission, ( 1888) p. 120; andjevons' " Investigations in Currency and
Finance," (1884) p. 95. The latter will be again referred to.
403]
Appreciation and Interest.
61
BERLIN RATES OF INTEREST IN REI.ATION TO RISING
AND FALLING PRICES. 1
Bank.
Market
Apprecia-
tion of
Money in
Commod-
ities.
a
Virtural
Interest in
Commod-
ities.
(Bank.)
h
Virtual
Interest in
Commod-
ities.
(Market.)
J2
1851-52
1853-57 ■
1858-64,
1865-70
1871-73
1874-79
1880-83
1884-88
1889-91
1892-95
4.0
4-7
4-3
4-7
4-5
4-3
43
3-6
4.0
3-4
3-7'
4.0
4.1
3-2
3-4
2.5
3-1
2.2
-1-5
-3-3
— 2.2
0.0
-4 I
+3.I
—0.1
+2.9
—1.4
+5-2
2.4
1.2
2.0
1.4
4.0
—0.2
6.4
3-3
5-5
1-7
7-5
Mean variation, 1858-91
• 4
2.1
In the foregoing table the relation is observed in six
out of nine sequences for bank rates (one being neutral)
and in six out of seven for market rates.
For France, index numbers covering a wide range of
articles are not available. Using those given in the Al-
drich report for sixteen articles, we have :
PARIS RATES OF INTEREST IN RELATION TO RISING
AND FALLING PRICES. 2
1861-64.
1865-70 .
1871-73.
1874-79 .
1880-86.
1887-90.
1891-95 ,
Bank.
5-1
3-2
5-3
3-1
3-2
3-1
2.6
46^
2.6
2.8
2.6
2.0
Appreciation in
Commodities.
+ 3-6
- 4.5
+ 43
+ 2.3
— 5-1
1 This table is constructed from the data in the Appendix. The
average in the second column, marked (i), is for the years 1861-64,
not 1858-64. The "appreciation" is calculated from the figures of
Soetbeer and Heinz, as given in the Aldrich report.
2 This table is constructed from the data in the Appendix. The
average in the second column marked (2) is for the years 1872-73, not
1871-73.
62
A?}!C7'ica?i Economic Association.
[404
Here the law is observed in five out of six sequences
for bank rates and three out of four for market rates/
It will be noted that the course of prices and interest
has been very similar in England, Germany and France.
For New York we have the following table :
NEW YORK RATES OF INTEREST IN RELATION TO RISING AND
FAI^IvING PRICES AND WAGES.2
0 i
0-°
I.S
in
1-1 —
0]
g-0
a C-I3
0 ^
ii'-S"
i!^?
OJ ,U!
ii.. (J
60
gv§
•■3 >.2
rt 0
CO:?
.9 2 a
•i^.§i^'
s 0 a
Call.
days
< u
s a 0
15^
3'-'—
t
I
a
a
J
-7
>
y
1849-57 • .
6.2
9.2
-3-8
-I.I
5-1
8.0
1858-60 . .
5.0
7-4
+b.4
— I.O
14-3
b-z
1861-65 . .
5-9
8.4
6.8
—20.2
-9-3
-13-5
— I4.S
-1.7
—3-1
1866-74 . .
5-4
8.4
7-5
-h4.7
-05
13-5
12.6
7-9
7.0
1875-79 • •
. .
5-1
+7.9
4-3-2
13-4
85
1880-84 • •
5-4
+0.6
—2.0
6.0
3-3
1885-91 . .
5-1
— 0 2
-1-3
4-9
3-7
1892-95 . .
4.6
.
Mean varia-
tion, '66-91
.6
3-8
2.1
We find here the same association of appreciation and
interest in all of the three sequences for call loans, in
two of the three cases for 60 days paper (the third being
neutral) and in three of the five cases for " prime " paper.^
This is with reference to commodities. The same holds
true in reference to wages. We find in the successive
periods that interest is high or low according to the degree
in which wages rise or fall. This is true in each of the
three sequences for call loans, in two of the three for 60
days paper and in three of the four, for " prime " paper.
^Assuming that prices fell, 1891-95.
'^ This table is constructed from the data in the Appendix. The
rates of appreciation are calculated from Falkner's figures for prices
and wages in the Aldrich Report.
3 Assuming that prices fell, 1892-95.
405] Appreciatio7i and Interest. 63
Perhaps the most remarkable fact in this table is
the extremely low rate for 1875-79. '^he average
is 5. 1 /^ which is the next but lowest in the table,
the lowest being 4.6% for 1892-95. The extra-
ordinary change in interest rates beginning in 1875
has been observed before ; but its connection with the
resumption act (as it seems to the writer) has been mis-
construed, Thus William Brough referring to that act
says : ^ " The mere announcement of our intention to
put our money on a sound metallic basis had brought
capital to us in such abundance that the resumption was
not only made easy, but the normal rate of interest was
reduced. . . . This remarkable reduction . . is ex-
plainable only on the ground of a large influx of foreign
capital." But this explanation would naturally require
a still lower rate of interest after resumption had been
accomplished. As the facts are the opposite, there
seems little room for doubt that the rate of interest was
simply accommodating itself in some degree to the rapid
appreciation involved in a return to specie payments.
§5-
The preceding statistics apply to gold standard
countries. Index numbers for silver standard countries
are not available prior to 1873. It is, however, a priori
probable that the relative price movements in gold and
silver standard countries before and after the rupture of
the bimetallic tie in 1874 presented a strong antithesis.
This event marked a change in gold standard countries
from rising to falling prices, while in silver standard
countries prices began to rise. Unless, therefore, prices
in silver countries had been rising previous to 1874, and
1 " Natural Law of Mouey," (New York, 1894), p. 124.
64
American Economic Associatio7i.
[406
rising very fast indeed, the antithesis referred to must
have existed. It is, consequently, of much interest to
inquire whether the fall in the rate of interest which
was so marked for gold countries was shared in equal
degree by silver countries. The following table for
periods of five years before and after the silver and gold
standards began to diverge, throws some light on this
problem.
AVERAGE BANK RATES IN GOI^D AND SILVER STANDARD COUNTRIES
BEFORE AND AFTER THE BREAKDOWN OF BIMETAI^USM.!
^
Tl
W u)
0
u^
0
iH tn
a
"" t!
a
3
0
0
a
a
0
.9"
_«■
0
lU 3
MO
11 i!
^5
0
fi,
0
u
cd
> u
tJ
fi
m
hT
m
&<
%
< -^
<
1870-74. .
5-1
16.4
10.6
3-7
4-5
4.9
7-5
10.7
5-2
1875-79- •
b.5
14.6
9.2
3-0
4.2
2.9
5-1
10. 1
3-y
While the results are not conclusive, they go to con-
firm our theory. In all gold countries the rate fell
after the par of exchange with silver countries was
broken, while in India it rose, and this in spite of the
flow of capital to India from England and other gold
countries. It is true that in Japan and China the rates
fell. But this fall was much less than in the gold
countries, whereas we should expect it to be much greater
if the only influence at work were the migration of
^Tbis table is constructed from the data given in the Appendix.
Bank rates are selected rather than market rates, as the latter are not
available for Calcutta and Shanghai. For New York, however, the
rates for " prime two name 60 days paper " are employed. Although
the United States and Japan were on a paper basis at the periods
given, the premium on gold in the one case and silver in the other
moved in opposite directions, affording, therefore, as great or greater
antithesis than if the standards had been simply gold and silver. For
the American premium see Chapter VIII, § 2 ; for the Japanese, see
Appendix, \ 3, note.
407]
Appreciation and Interest.
65
capital. Such extraordinary rates as ruled in China and
Japan in the '70's must have been extremely sensitive to
the influence of an influx of capital. Even though
British investment in Japan or China may have been
much less than in India, we should expect its tendency
to reduce the native rate of interest to be more effective
where that rate was 10^ or 15 ^ than where it was 5 ^.
An added reason for a fall in rates in Shanghai and
Tokyo is the narrowness of the areas affected by foreign
capital, which, having little opportunity to penetrate
inland, tends to glut the market in the open ports.
Turning to the period for which index numbers are
available, we have the following table for India, Japan
and China.
RATBS OF INT:EREST IN R^I/ATION TO RISING AND FAI^LING PRICES
IN CAI,CUTTA, TOKYO AND SHANGHAI.i
Bank.
Market.
Appreciation in
Commodities.
Calcutta ....
1873-75
1876-78
1879-85
1886-89
1890-93
5-3
6.8
5-9
6.0
4-3
+2.6
— II.O
+3-8
-2.6
-4-7
Tokyo
1873-77
1878-81
1882-86
1887-93
14.0
16.3
12.8
9-3
12.0
12.2
10.3
9-4
—0.2
-13-3
+10.4
-2.8
Shanghai. . . .
1874-81
1882-88
1889-93
91
7-5
7.0
5.8^
5-8
-1-4
+1.3
-0.9
Here we find our theory confirmed in three out of
four cases for India, two out of three for bank rates in
Japan, and two out of three for market rates, one out of
two for bank rates in China, while the one case for
market rates is neutral.
'This table is constructed from the data given in the Appendix.
The entry marked (i) is for 1885-88, not 1882-88.
66 American Economic Association. [408
Summarizing the cases for the seven countries exam-
ined, we find 57 favorable, and 16 unfavorable, to our
theory, distributed as follows :
Eng-
land.
Ger-
many.
France.
United
.States.
India.
Japan.
China.
Total
Favorable . .
21
12
8
8
3
4
I
57
Unfavorable .
5
3
2
2
I
2
I
16
We therefore conclude with great confidence that,
" other things being equal," the rate of interest is high
when prices are rising and low when prices are falling.
We turn next to the question hozv far the rate of in-
terest has been adjusted to price movements. The for-
mula (1 + /)=(! + 2 )(i +'^) or its more convenient
form for present purposes, / ^ / + « + ia., enables us to
calculate the rate of interest in the commodity standard
which was equivalent to the money interest paid in each
period. Thus in London for 1826-29 the rate of inter-
est ( z ) in money was 3.5 %, but money was appreciating
relatively to commodities 4.2 ^ ( « ), so that the interest
actually paid in terms of commodities (z. ^., the forty
commodities averaged by Jevons) was / = .035 + .042
+ .035 X .042 = 7.8^. It will be seen from the table
in § 3 that the virtual rate of interest paid in commod-
ities usually varies inversely with the rate paid in money.
For 1853-57, money interest was 5.3% and for 1891-95,
1.6^ but commodity interest for 1853-57 was 2.8^ and
for 1891-95, 5.5^. Moreover commodity interest fluc-
tuated much more than money interest, the mean varia-
tion from the average being for money interest .7 ^, and
for commodity interest, 2.6^. All these facts suggest,
— indeed practically demonstrate — that money interest
was not adequately adjusted. It is of course not to be
409] Appreciation arid Interest. 67
assumed that commodity interest ought to be invariable,
but we can be practically certain that its variations ought
not to be three and a half times the variations in money
interest. Such fluctuations must mean that the price
movements were inadequately predicted. If any doubts
were possible on this point they must disappear when
we find that for 1871-73 commodity interest was minus
2.7^. Money lenders would have been better off had
they simply bought commodities in 1871 and held them
till 1873. Such losses are especially apt to appear in
short periods. Thus if we take the period 1824-25, we
find that the market rate was Z-l%i ^^^ '^^te of appreci-
ation was minus 14.5% and the virtual rate of interest
in commodities minus 11. 2,%.
The same observations apply to the rates at Berlin,
Paris, New York, Calcutta, Tokyo and Shanghai. In
New York during the inflation period 1861-65, com-
modity interest sank to the fabulously low figure of -14.8
fo , though the rate of interest in the labor standard was
only -3. 1 fo . This shows in a striking way how thor-
oughly the greenback inflation upset all business cal-
culations. This fact has generally been recognized,
though probably underestimated. It is amply confirmed
by examining the predictions as to the termination of
the war and the reduction of the gold premium which
were recorded from month to month in the " Notes on
the Money Market " in the ( New York ) Banker's Maga-
zine. In all probability this is always true of pe-
riods of paper money inflation. Our tables show it for
the Japanese inflation of 1878-81.
§7
We can now understand why a high rate of interest
need not retard trade nor a low rate stimulate it. These
68 American Economic Association. [410
facts have puzzled many writers. For instance,' " Public
inquiry has been of late strongly directed to the reasons
for the very low rate of interest upon loanable capital
in the year 1875, the more especially as ten years ago
the very high rates then prevailing created equal sur-
prise. " Again,^ " The effect of such and many more
changes effected during the last twenty years or so, is
seen in a general increase in wealth and of mercantile
industry and profits. Thus only can be explained the
extraordinary high rate at which the interest of money
has in the last ten years often stood. During 1854-57
the rate of interest was only for a few months below
5 fc , but for many months above it. For more than half
a year it stood at 6 and 7^, and in the end of 1857 it
remained for nearly two months at \o%. Again, in
1861, interest rose to 6 and 8^, and all this, to the S2ir-
prise of the elder generation.^ without the general stop-
page of trade., the breach of credit., and the flood of
bankruptcy., which has hitherto attended such rates of in-
terest. It is certainly not to increasing scarcity of cap-
ital we should attribute such rates, but rather to a greatly
extended field for its profitable employment. " ^ But
were these rates high ? If we turn to our table for Lon-
don rates we find that the average market rate for
1853-57 ^o^s appear to be the highest in the table but,
unmasking it of the money element, we find it is
equivalent to a commodity interest of 2.8^. This is
i.o^ lower than the average for the whole period, 1826
-95. Should we be surprised that industry did not lan-
guish ?
'Robert Baxter, Journal of the Royal Statistical Society, June, 1S76.
'^Jevons, " Investigations, " p. 95. The italics are the present
writer's.
^This view had also been expressed by TookeandNewmarch, " His-
tory of Prices ", Vol. V, p. 345.
41 1] Appreciation and Inte^'est. 69
Professor Bonamy Price^ writing at a time of very low
interest rates says : " Everyone remembers the agitations
associated with 7^, the trepidation of merchants, the
apprehension of losses in business. ... If only a
moderate rate could be reckoned on as steady, how happy
would everyone have been ! . . . Yet what are the facts
and feelings today? Is every merchant, every manu-
facturer rejoicing in the pleasant terms on which he ob-
tains the accommodation so necessary for his business ?
. . . Alas ! no such sounds meet our ears. . . . Com-
mercial depression is the universal cry, depression prob-
ably unprecedented in duration in the annals of trade,
except under the disturbing action of a prolonged war.
In the export figures, the writer still fails to see
any signs of the long-looked-for revival of trade. Both
quantities and values continue to shrink in all save a few
cases. . . . What then is the cause ? The explajta-
ation will certainly not be found in gold nor in any form
of currency whatever. . . . nor has anyoize said
anything so ridiculous. . . . That cause is one and
one only : over spending. "
If we turn back to our London table we find, however,
that for 1874-79 the commodity rate of interest was
7. 1 % ! It would be astonishing if trade did not shrink
under such a burden.
All these writers mistook high or low nominal inter-
est for high or low real interest. Tooke apparently did
the same. In his " History of Prices ", vol. ii, p. 349,
he names as the last of six reasons for the fall of prices
for 1814-37, "a reduction in the general rate of inter-
est. " This is probabl}^ not only an inversion of cause
and effect, but also, when the veil of money is thrown
1" One per cent ", Contemporary Review, April, 1877. The italics
are the present -writer's.
70
American Economic Association.
[412
off, a mis-statement of fact. The commodity interest for
1826-29 was 7.8%. It Avould seem that Tooke, Price,
and Jevons all overlooked the fact that interest, unlike
prices, is not an instantaneous but essentially a time phe-
nomenon.
§8.
In order to make our results as certain as possible, the
following table is formed in which the longer price
movements are selected. It consists of three periods, of
ten, twelve, and twenty-one years respectively.
LONDOISr MARKET RATES OF INTEREST IN REI^ATION TO RISING
ANT) FALLING PRICES, WAGES, AND INCOMES.i
Market
interest.
i
Apprecia-
tion of
Money in
Commod-
ities.
a
Virtual
interest
in
commod-
ities.
/
Apprecia-
tion of
Money in
Labor.
a
Apprecia-
tion of
Money in
Income.
a
Virtual
interest
in
Labor.
y
Virtual
interest
in
Income.
J
1826-35
1853-64
1874-95
3-4
4.6
2.4
+ 1.2
-0.9
-1-2.4
4.6
3-7
4-9
1860-74
1874-91
4.0
2.7
— 2.1
0.0
-2.5
—0.2
1.8
2.7
1.4
2.5
In averages covering so many years, we may be sure
that accidental causes are almost wholly eliminated.
We find that during the period of rising prices, 1853-64,
the average rate of interest was 2.2^ above the average
for the subsequent period of falling prices, 1874-95, and
1.2^ higher than in the former period of falling prices,
1826-35. The rates in the commodity standard how-
ever vary in the inverse order, the highest interest being
for 1874-95 and the lowest for 1853-64. It is a note-
worthy fact, in strong contrast with what we have found
' The rates of appreciations in labor and income are based on
" Changes in average wages in the United Kingdom between i860
and 1 89 1," by A. L,. Bowley, in the Journal of the Royal Statistical
Society, June, 1895.
413] Appreciatio7i and Interest. 71
true of sliort periods, that the commodity interest in this
table of long periods is less variable^ than the money
interest. Thus the adjustment of (money) interest to
long price movements is more perfect than to short.
§9.
The foregoing table shows exactly how the English
borrower has fared so far as commodities and labor are con-
cerned. During 1853-64 he paid 2^-1% in commodities
but during 1874-95 he had to pay 4.9%, an increase of
1.2%. In the labor standard, during 1860-74, he paid
1.8%, and during 1874-91, 2.7%, showing an increase of
.9%, while in the income standard the rates were 1.4%,
and 2.5% respectively, showing an increase of 1.1%.
Now it is quite conceivable that commodity interest
should normally be high during the latter period, if this
period can be shown to be one of unusually rapid
economic progress.^ That this was in fact the case has
^ The mean variation for the three money rates is easily seen to be
.8% and for the commodity rates only .5%. The two "labor" and
" income" rates differ by .9 and 1.1% while the money rates differ
by 1.3/3- In the New York table which follows, the money rates
differ by 3.0% and the commodity rates by 3.2%, but the labor rates
by only 2.2%.
'-^ For when the future seems a time of relative plenty, future goods
may be discounted at a high rate and profits measured in commodi-
ties may be large. Contrariwise during a period of progressive
scarcity commodity interest may be normally low. These theories
may seem to conflict with current opinion ; but only when the funda-
mental distinction is overlooked between a period of plenty and a
period of progressive plenty, and between a period of scarcity and a
period of progressive scarcity. During stationary scarcity and
stationary plenty, normal commodity interest may be high and low
respectively. But during the transition from scarcity to plenty in-
stead of running through the intermediate rates, commodity interest
may be normally higher than in either of the extreme states. This
is a case in which " dynamic" economics differ strikingly from
"static" economics.
72 American Economic Association. [414
been pretty thoroughly established by the admirable
researches of David A. Wells ^ and others, and by the
statistics of wages compiled by Falkner ^ and Bowley."
But these considerations can scarcely apply to " labor
interest" or " income interest." A man who borrowed
the equivalent of a hundred days' income during 1860-74
could pay it back in a year with the equivalent of 101.4
days' income, while during 1874-91, for a similar loan
he must return 102.5 days' income. This is the opposite
of what we should expect as the influence of prog-
ress. It therefore seems safe to ascribe at least 1.1%
as the borrower's loss since 1874, compm^ed with his
gain or loss before 1874. It may well be that part
of this comparative loss for 1874-91 represents a gain
for 1860-74. If we ascribe half to this gain, there
remains the other half, .5% or .6%, as loss during
1874-91. Although this division is quite arbitrary
the conclusion that the borrower's loss was at least
Yz'^/o seems reasonable when we consider that the
total comparative loss, 1.1%, was itself a minimum.
But even if we suppose the debtor's gain during the
former pferiod twice his loss during the latter, (a supposi-
tion which, in view of all the facts, must be within the
claims of all reasonable monometallists) we still have a
minimum (English) debtor's loss since 1874 of ^%.
Combining the results just given with those of Chap-
ter IX we see that the average loss to English borrowers
during the fall of prices since 1874-75 probably lies be-
' " Recent Economic Changes," (New York, 1890).
^ Lac. cit. These statistics, taken in connection with price statistics,
show that commodity wages, i. e., money wages divided by the index
number of prices (z£/Ao/(?5a/^ unfortunately), rose in England during
1860-74 at the rate of 1.8% per annum and during 1874-91 at the rate
of 2.2%, while in America for 1849-57 they fell 2.7% per annum and
for 1875-91, rose 2.4% per annum.
415] Appreciation and Interest. 73
tween yi'^/o and ^% and almost certainly between ]A,^o
and 1%. The former result may be stated thus,
y^± yi% and the latter, ^ d= >^%. We may therefore
say with considerable confidence that the average debt-
or's loss in England for contracts made since 1874-75,
has been two-thirds of one per cent, per annum with a
possible error of one-third of one per cent. In other
words, the average debtor's loss could have been cor-
rected by a reduction in the rate of interest of from
one-third of one per cent, to one per cent.
§ 10.
For contracts made before 1874, but continued to the
present, the loss, since 1874, must have been greater.
We may therefore accept the former estimate of ^ % as a
lower limit or, to be safe, 5^ %. To find an upper limit,
we recur to the fact that India gold bonds purchased
prior to 1875 yielded very nearly ^ % more interest than
the average subsequent to that date. Since we have
estimated that the average from 1875 was at most i %
too high, the average for periods beginning before but
ending after 1875, must have been at most i ^ % too high,
for it can scarcely be claimed that the rate of interest for
the part of the term of the bonds previous to 1875 ought
to have been lower than that for the part subsequent to
that date. We therefore conclude that, for English con-
tracts made before 1874-75, the debtor's loss since 1874-
75 has been between ^% and i>^%, i- <?., i d= ^%.
It follows that for contracts which were made prior to
1874-75 but subsequently converted or continued at a
lower rate of interest, the loss since 1874-75 was
I d= >^% per annum to the date of conversion and
^ d= >^ % since that date.
74
American Economic Association.
[416
It should be observed that the foregoing calculations
are based on public prices of bonds and rates on money.
Interest on private loans and farm mortgages, although
influenced ^ by the same causes which affect the money
market, is less flexible and the debtor's losses or gains
in these cases are doubtless somewhat greater.
§11.
The following table gives the long time averages for
New York. The war period is omitted and a nine years'
period of rising prices is compared with a seventeen
years' period of falling prices.
NEW YORK RATES OF INTEREST IN REI.ATION TO RISING AND
FALLING PRICES AND WAGES.
Interest Appreciation
Prime of money
Two name | in
60 days. jcommodities.
i a\
Appreciation
of money
labor.
Virtual
Interest
in com-
modities.
j\
Virtual
Interest
labor.
h
1849 - 57 •
1875-91 .
8.2^
5-2
-3-8
+2.0
-I.I
-0.4
4.1
7-3
7.0
4.8
We find for 1849-57 and 1875-91 that the money rates
were 8.2 and 5.2%, the commodity rates 4.1 and '].'^%^
but the labor rates 7.0 and 4.8%. We see therefore,
that in terms of labor, loans in America have actually
been easier during 1875-91 than during 1849-57. This
fact suggests the conclusion that the debtor's loss in
America has not been as great as in England. This, if
^ See Appendix, \ 2, 4th title.
'^The average of Elliott's figures (which are not for "prime" paper)
is 9.2, but i.o has been deducted from this average in order that it
may be properly compared with the average of Robbins' figures for
1S75-91. The correction is based on the fact that i.o was the average
excess of Elliott's figures over Robbins' during the fifteen years,
1860-74. See Appendix.
417] Appreciation and Interest. 75
true, may be due to a more rapid rate of progress in the
United States/
§ 12.
Four general facts have now been established :
(i) High and low prices are directly correlated with
high and low rates of interest ; (2) Rising and falling
prices and wages are directly correlated with high and
low rates of interest ; (3) The adjustment of interest to
price (or wage) movements is inadequate ; (4) This ad-
justment is more nearly adequate for long than for short
periods.
These facts are capable of a common explanation ex-
pressing the manner in which the adjustment referred to
takes place. Suppose an upward movement of prices
begins. Business profits (measured in money) will rise,
for profits are the difference between gross income and
expense, and if both these rise, their difference will also
rise. Borrowers can now afford to pay higher " money
interest." If, however, only a few persons see this, the
interest will not be fully adjusted ^ and borrowers will
realize an extra margin of profit after deducting interest
charges. This raises an expectation of a similar profit in
the future and this expectation, acting on the demand for
loans, will raise the rate of interest. If the rise is still
^ See page 72, note 2.
^ It seems scarcely necessary to add as an independent cause of mal-
adjustment the accumulation (or in the opposite case, depletion) of
bank reserves, for this is but another symptom of mal-adjustment due
to imperfect foresight. An increase of gold supply, as in 1852-53
(see Tooke and Newmarch, "History of Prices," vol. V, p. 345)
may first find its way into the loan market instead of into circulation.
But if foresight were perfect, this would not happen, or if it did hap-
pen, borrowers would immediately take it out (or increase the liabil-
ities against it) to avail themselves of the double advantage of low
interest and high prospective profits from the rise of prices about to
follow.
76 American Economic Association. [418
inadequate the process is repeated and thus by continual
trial and error the rate approaches the true adjustment
When a fall of prices begins, the reverse effects ap-
pear. Money profits fall. Borrowers cannot afford to
pay the old rates of interest. If, through miscalculation
they still attempt to do this, it will cut into their real
profits. Discouraged thus for the future, they will then
bid lower rates.
Since at the beginning of an upward price movement,
the rate of interest is too low, and at the beginning of a
downward movement it is too high,^ we can understand
not only that the averages for the whole periods are im-
perfectly adjusted but that the delay in the adjustment
leaves a relatively low interest at the beginning of an
ascent of prices and a relatively high interest at the be-
ginning of a descent. This would explain, in part at
least, the association of high and low prices with high
and low interest.^ The fact that the adjustment is more
perfect for long periods than for short, seems to be be-
cause in short periods, the years of non-adjustment at
the beginning occupy a larger relative part of the whole
period.
§ 13-
What has been said bears directly on the theory of
"credit cycles." In the view here presented periods of
speculation and depression are the result of ifiequality
of foresight. If all persons underestimated a rise of
price in the same degree, the non-adjustment of interest
would merely produce a transfer of wealth from lender
to borrower. It would not influence the volume of
loans (except so far as the diversion of income from one
person to another would itself have indirect effects, such
' These facts may be verified from the tables in the Appendix.
-" Cf. I 2.
419] Appreciatio7i and Interest. 77
as bankruptcy). Under such circumstances the rate of
interest would be below the normal, but as no one knows
it, no borrower borrows more and no lender lends less
because of it. In the actual world, however, foresight
is very unequally distributed. Only a few persons have
the faculty of always " coming out where they look."
Now it is precisely these persons who make up the bor-
rowing class. Just because of their superior foresight
society delegates to them the management of capital.
It is they who become "captains of industry." Their
share consists of profits (or losses) while others lend
them capital and receive interest or commuted profits/
It therefore happens that when prices are rising, bor-
rowers are more apt to see it than lenders. Hence,
while the borrower is willing to pay a higher interest
than before for the same loan, lenders are willing to loan
the same amount for the same interest. That is, the
" demand schedule " ^ will rise while the " supply
schedule " remains comparatively unchanged. This
will of course raise the rate of interest. But it will also
cause an increase of loans and investments.^ This con-
stitutes part of the stimulation to business which bi-
metallists so much admire.
When prices fall, borrowers see that they cannot em-
ploy " money" productively except on easier terms, but
lenders do not see why the terms should be made easier.
In consequence " entrepreneurs" borrow less, enterprise
^ Hadley, " Interest and Profits," Annals of the American Acade-
my of Political and Social Science , November, 1893; also "Econom-
ics," (New York, 1896), pp. 116, 269.
^Marshall, "Principles," Vol. i, (3rded.) p. 171.
^ That this and the corresponding statement in the next paragraph
are borne out by facts appears to be confirmed, so far as bank loans
and discounts are concerned, by Sumner, "History of Banking in
the United States," (New York, 1896) and Juglar, " Crises commer-
ciales," (Paris, 1889).
78 American Economic Association. [420
languishes and, though interest falls in consequence of
decrease in demand, it does not fall enough to keep the
demand from decreasing/
If lenders, as a class, were possessed of greater fore-
sight than borrowers, we should find trade languishing
during rising prices and stimulated during falling prices.
In the former case lenders would require high interest
for fear, as in 1871-73, they were lending at a loss of
real wealth, while borrowers would be afraid of the ap-
parently high rates charged ; and in the reverse case
lenders would be eager to reap the benefits of an appre-
ciating standard while borrowers, deceived by the appar-
ently low rates, would rush in to profit by them.
We see therefore, that while imperfection of foresight
transfers wealth from creditor to debtor or the reverse,
inequality of foresight produces over-investment during
rising prices and relative stagnation during falling prices.
In the former case society is trapped into devoting too
much wealth to productive uses and in " long production
processes " ^ while in the contrary case under-in vestment
is the rule. It does not seem possible to decide the ques-
tion which of the two evils is the greater. ^
^ President Andrews in "An Honest Dollar," p. 3, writes : "Interest
is low . . not because money is abundant as before, but because it is
not, its scarcity having induced fall of prices and so paralysis in in-
dustry." But it should be added, the cause of the fall of interest is
primarily the expectatio7i of small profits. Cf. infra.
- Professor Bohm-Bawerk, (" Positive Theory of Capital, " p. 335),
writes : " Now the constant presence of the agio on present goods is
like a self-acting drag on the tendency to extend the production pe-
riod. Extensions which would be harmful as regards social provis-
ion are thus made economically impossible. " During rising prices
this drag presses too lightly and during falling prices too heavily.
■^ Bimetallists usually claim that falling prices are the greater evil .
For arguments on both sides see Professor Marshall's evidence,
Report on Depression of Trade, (1886), p. 422.
42 1] Appreciation and Interest.
79
It is believed that the foregoing theories correspond
closely with observed facts as to business stimulation
and depression, volume of loans, etc., but it is not pro-
posed here to enter upon a special statement of them/
Nor is this the place to treat fully the reaction on prices
themselves. But it can scarcely be doubted that the
mal-adjustment of interest is a central feature in the
whole movement. Professor Marshall, who recognizes
fully the distinction between money and commodity in-
terest, says : ^ " When we come to discuss the causes of
alternating periods of inflation and depression of com-
mercial activity, we shall find that they are intimately
connected with those variations in the real rate of inter-
est which are caused by changes in the purchasing
power of money. For when prices are likely to rise,
business is inflated, and is managed recklessly and waste-
fully ; those working on borrowed capital pay back less
real value than they borrowed, and enrich themselves at
the expense of the community. When afterwards credit
is shaken and prices begin to fall, everyone wants to get
rid of commodities and get hold of money which is rap-
idly rising in value ; this makes prices fall all the faster,
and the further fall makes credit shrink even more, and
thus for a long time prices fall because prices have
fallen."
We would add that these effects of credit could not
follow if the interest rate were perfectly adjusted. In-
terest, rather than credit, appears as the chief independ-
ent variable, objectively speaking, though behind it all
is imperfection of foresight.
^See Report on Depression of Trade, 1886; and Report of the
Gold and Silver Commission, 1888.
2 " Principles of Economics ", Vol. I, (3rd ed., 1S95), p. 674.
PART III. APPLICATIONS.
CHAPTER XL
THE BIMETALLIC CONTROVERSY.
§1.
It is not the purpose here to follow all the arguments
for and against bimetallism, but merely to outline the
bearing of the foregoing theories and facts upon some of
those arguments.
We have seen in theory and in practice that the rate
of interest has tended to accommodate itself to the
changing value of money. It follows that it is quite er-
roneous to obtain the amount of the debtor's or creditor's
loss by merely reckoning the effect of appreciation or
depreciation on \}i\^ principal of the debt.
And yet, after all allowances are made, it is true that
there remains a net loss alternating between debtors and
creditors according to the varying tides of credit and
prices. During the last twenty years it has happened
that the debtor was on the losing side. We have estimated
his average loss at ^ + ^ % per annum in England and
probably less in this country. This loss is not inconsid-
erable. When looked at in the aggregate it appears
very large indeed. The minimum net indebtedness
public and private in the United States is given at 20
billions,^ on which ^% would amount to 130 millions
per annum. But when we compare this with the aggre-
' G. K. Holmes, Bulletin of the Department of Labor, November,
1895, p. 48.
423] Appreciation and Interest. 81
gate principal involved or with the 14 odd billions ^ of an-
nual product, it does not seem capable of the deep social
harm attributed to it. In fact it is always misleading to
consider aggregates except in comparison with each
other. Applied to an ordinary two months' loan of
$1,000, % % amounts to one dollar. In New York city
the up-town banks often charge a rate more than ^ ^
higher than that of the down-town banks without driving
away customers.
§ 2.
The ordinary estimates of the debtor's loss are based on
index numbers. From Sauerbeck's tables it appears that
between 1873 ^^^ ^895 money appreciated in terms of the
commodities selected, 79.0%, which is at therateof 2.7%
per annum. This is from three to eight times as much as
the estimate we have made. The error of the ordinary
calculation does not consist simply in neglecting the
matter of interest. The use of index numbers is itself
subject to fatal objection.^ When unchecked by other
statistics they are very misleading. Not only do we
reach different results according to the number of com-
modities and the method of averaging,^ but the very best
methods fail to give a trustworthy measure of ordinary
domestic purchasing power, both because they are based
on wholesale instead of retail prices and because they
ignore expenditure for house rent and for labor and
domestic service, which, in the family budgets of those
who borrow and lend, must form a very large item.
^ Edward Atkinson, Engineering Magazine, December, 1895.
^ The reader is reminded that, though we have used index numbers
to determine " commodity interest, "^we have not employed them to
estimate the debtor's loss.
^See articles by Edgeworth, Sauerbeck and Pierson in the ^co«o w«^
Journal, March, June, and September, 1895, and March, 1896.
82 American Economic Association. [424
Moreover to know the purchasing power of a dollar does
not enable us to know the " subjective value" or mar-
ginal utility of money. The number of dollars at com-
mand ( /. ^., money incomes) must also be considered.
And even were our knowledge complete as to the
marginal utility of money as well as its purchasing
power, we should be as far as ever from solving the
problem of the debtor's loss. The question is not one
of appreciation of gold relatively to commodities or to
labor or any other standard. It is, as we have seen,
exclusively a question of foresight and of the degree of
adaptation of the rate of interest.
§3-
It scarcely needs to be pointed out that bimetallism
can only affect unpaid debts. We should therefore
clearly recognize the fact that the most of the loss which
debtors have suffered since 1873 has already passed be-
yond the reach of remedy. Of the residuum the losses
vary with the duration of the debt. On debts three
years old the loss in England is probably about two per
cent., on those six years old about four per cent., and so on.
Moreover, on debts contracted before the fall of prices
began, the annual rate of loss was greater, being proba-
bly, as we have seen, i ± /^%. Most such debts, how-
ever, including even national debts, have received part
of the benefit of low interest through extensive con-
versions.
Now bimetallism, if adopted, so far from rectifying
gains and losses, would simply increase the inequalities.
If it resulted in debasing the standard ten per cent, it
might exactly remedy debts fifteen years old, but the
correction would be too small for those older and too
425] Appreciation and Interest. 83
large for those younger than fifteen years. The latter
form the great bulk of existing indebtedness. The
average life of a farm mortgage is 4^ years ^ so that
the average age of mortgages now in force would be
about ^Yi years. Bank loans run only a few days or
months. These and other short time loans make up
some sixty per cent, of existing indebtedness.^ The re-
mainder consists of railway and government loans and
few of them extend back to 1873.^ '^\i^ chief and
dominant effect of debasement would therefore be to
defraud the lender of today and yesterday.* The older
debts, for which the remedy is designed, no longer exist.
§4.
But even if bimetallism or any other financial scheme
could so scale debts as exactly to counteract the losses
connected with the fall of prices, the ethics of such an
arrangement ought not to go unmentioned. The fact
that debtors have lost does not imply that they have suf-
fered an injustice. If a man insures his house and it
burns the next day the insurance company suffers a loss
but not an injustice. If the company should ask for leg-
islative relief on the ground that it had not expected so
sudden a termination of its policy, that the fire was
brought about by causes which it could not possibly
foresee or provide against, it would be laughed to scorn.
" Keep your contract " would be the reply. It would
^ 'Eleventh Census, Bulletin 71.
'^Holmes, loc. cit.
^ Probably mucb less than one- fourth for American railways. This
estimate is made by looking over all the funded indebtedness whose
dates of issue are given in the " Ofl&cial Intelligencer" for 1894.
* For effects on "Social Classes," see article by Professor H. W.
Farnani, Yale Review^ August, 1895, p. 183.
84 American Economic Association. [426
make no difference if the fires were nniversal, and every
insurance company lost. Those who assume the risks
must take the consequences. A farmer mortgages his
farm and agrees to pay $1,000 and 5% interest. By the
terms of the agreement he takes all risks as to what the
dollar will buy of wheat or anything else. He may lose
and all farmers may lose and the causes may be in India
or Australia or in the sun spots, but we can scarcely af-
ford to surrender the ancient principle of the Inviolabil-
ity of Contracts, through sympathy with the misfortunes
of any individual man or group of men. That elements
of risk exist in every contract and that this risk implies
responsibility are too often ignored. President Andrews
writes ^ : " Increase in the value of money robs debtors.
It forces every one of them to pay more than he cove-
nanted [!] — not more dollars but more value." But
contracts which call for money do not call for " value "
any more than contracts to deliver wheat call for money.
If a man had agreed a year ago to deliver 10,000 bricks
to a builder at a fixed price, he would not be justified in
offering only 9,000 on the ground that the price had
gone up. A contract to pay " value " would be a legal
curiosity, and the court which should attempt to inter-
pret it would hear an interesting assortment of defini-
tions from our leading economists.
Closely associated with the principle of the Inviolabil-
ity of Contracts is the principle against retro-active
laws, and in particular, against laws which alter existing
contracts. The world has reached these principles
through a long and weary struggle and much costly ex-
perience with repudiation and the abuses of legal tender.
The burden of proof rests on those who would revert
^ " An Honest Dollar, "p. 2.
427] Appreciation and Interest. 85
to these experiments for the sake of any benefits from
bimetallism. Surely the practical reasons against such
a course are obvious enough. When once a government
has undertaken to " correct " debtor's losses, it will not
stop at one attempt. History teaches that a nation once
embarked on such a policy never keeps its most solemn
word as to where it shall leave off. ^ Creditors will fear
to lend except at usurious rates and the debtor of the fu-
ture will pay dearly for the emancipation of the debtor
of the present.^
§5-
To those who claim that the cause of the aggravation
of debts was governmental action in the first instance
and that therefore it is now a fit subject for governmental
correction, the obvious answer is that this does not ap-
ply to the great mass of existing contracts which have
been formed since demonetization.
Finally it may be objected that the gold standard as
such is on the side of creditors as against debtors because
it is an appreciating standard and according to our own
statistics the debtor usually wins in rising and loses
in falling prices.
Such reasoning, however, is entirely fallacious. The
fallacy is of the same kind as that contained in the fa-
cetious advice to young speculators : " Buy when stocks
are low and sell when they are high. " It is easy to
prophesy after the event ; investors in India silver bonds
have lost for twenty years but this does not prove that
the present price of rupee paper is still too high. If it
did, London brokers would be the first to know it and
1 Shaw, " History of the Currency," (18951 ; also Sumner, " History
of American Currency," p. 331.
2 See the writer's "Would Bimetallism benefit the 'Debtor Class'?"
The Bond Record, April, 1896.
86 American Economic Association. [428
correct it. We cannot therefore say the " present
arrangement is all in favor of tlie creditor and against
the debtor. " What bimetallist will risk his reputation
in predicting the course of prices and interest in the
next twenty years ? If prices rise, we may with great
probability predict that the debtor will vrin. If they
fall, he will lose. But who knows which is the true
§6.
Legislation to offset the effects of a fall of prices in
the past is wrong, because retro-active. Legislation to
offset the effects of a fall in the future is absurd, because
we cannot know there will be a fall, and if we could,
there would be no need of legislation.
There remains to be considered legislation for the
purpose of making the monetar}- unit less variable, that
is, not to prevent something which we can foresee but
to prevent something which we cannot foresee. Such
a reason for monetan,- legislation must be recognized
at once as thoroughly sound. But it applies equally
well to " symmetallism" ^ and other plans - for monetary
reform.
That bimetallism ( as long as it lasted)^ would be
' Edgewortli, " Thoughts on monetary reform", Economic loiirnal,
September, 1S95.
'E.g., the multiple standard propounded by Lowe, 1S22, and
Scrope, 1833, and advocated by Jevor.s, "Money and the Mechanism
of Exchange", p. 328, and "Investigations", p. 123, and by Marshall,
Report of the Commission on Depression of Trade, p. 423 ; also
the various forms of double standard suggested by Marshall, ibid.,
Edgeworth, ibid., Hertzka " Das iuternationale Wahrungsproblems,"
1892, and Stokes, "Joint Metallism," (1S95) ; also the various forms of
elastic currenc}* suggested by Professor Walras, " Theorie de la
Monnaie", (Lausanne, iSS5i, by Secretary Windom and others.
'See the writer's " Mechanics of Bimetallism," Economic Journal,
September, 1894.
429] Appreciation and Interest. 87
more dependable than monometallism is probable on
a priori grounds, but the statistics which we have given
seem to reveal as great uncertainty in price movements
before 1873 ^^ since. It is indeed a large question
how far au}^ sort of monetary' reform could remedy the
matter ; for the expansion and contraction of credit
might be almost as violent and mischievous as ever. It
may be however, that " the evils . . are so great that it
is worth while to do much in order to diminish them a
little." ^ If a more stable and less expensive ^ monetary
standard can be found, it will be an inestimable boon to
the civilized world. As an improvement on the two
single standards now existing, bimetallism, launched at
the market ratio, ma}" be worth serious consideration.
But the proposal now before the world is bimetallism at
15/^ or 16 to I. Such bimetallism means debasement
of the standard of any single country- which attempts it.
If international, it means debasement in gold standard
countries, and a violent contraction and appreciation in
silver standard countries. In no other wa}- could the in-
fluence of the legal ratio on the market ratio be felt. We
should witness not only losses to creditors in the former
countries but losses to debtors in the latter, and these
losses would be far in excess of those which we have
found to follow from the slow" and half foreseen appre-
ciation of the last tv^'enty years.
'Marshall, "Principles of Economics" Vol. I, 3rded., (1895), p. 674.
*Jevons, "Investigations," p. 104; " . . the very scarcity of gold
is its recommendation . . in itself gold digging has ever seemed
to me almost a dead loss of labor as regards the -world in general."
Also Lexis, Economic Journal, June, 1S95, p. 276.
CHAPTER XII.
THE THEORY OF INTEREST.
§1.
The relation existing between interest and appreciation
implies that the rate of interest is relative to the standard
in which it is expressed. Economists, from Hume and
Adam Smith down, seem to have considered the money
element entirely eliminated from the rate of interest by
the simple fact that, in the last analysis, it is capital,
not money, which is loaned and returned. But, as
has been seen, we can identify the rate of interest in
terms of capital with the rate of interest in terms of
money only when the price ratio between money and
capital remains constant.
The first thought suggested by this fact is to dis-
tinguish between " nominal" and " real" interest in the
same way that we distinguish between " nominal" and
" real" wages. This seems to be the thought of all the
writers who have touched on the subject. Professor
Marshall in fact uses the words " real" and " nominal."^
de Haas speaks of the effect of the appreciation or de-
preciation of money as introducing a " third element"^
into the rate of interest. This " element" is to be added
to or subtracted from the sum of the other two elements,
which are a payment for capital (or the rate of interest
proper) and a payment for insurance. John Stuart Mill
' "Principles of Economics," Vol. I, 3rd ed. (1S95), P674.
''■Journal of the Royal Statistical Society, March, 1S89. It will
be seen from the formula i-l-7"=(i + 0 (i + a) that the "third
element" is not a mere additive term.
43 1] Appreciation aiid hiterest. 89
and the eighteentli century pamphleteer ^ were evidently
thinking of a normal rate of in terest in coin to which
a certain extra charge is to be added if paper depreciates
in reference to coin. Finally the article of Professor
John B. Clark ^ is devoted chiefly to a search for an ab-
solute standard to which we may refer any monetary
appreciation or depreciation and in which therefore
" real" interest could be expressed. It is not denied
that the words " real" and " nominal" are very conven-
ient terms and for a rough and ready expression may
serve a useful purpose. But the mere distinction be-
tween "real" and "nominal" is quite inadequate for a
true and accurate statement of the case.^
If we seek to eliminate the money element by ex-
pressing the rate of interest in terms of real " capital,"
we are immediately confronted with the fact that no two
forms of capital maintain or are expected to maintain a
constant price ratio. There are therefore just as many
rates of interest on capital as there are forms of capital
diverging in value. Even if we could find an ideal in-
dex number for capital in general or for commodities,
there are other kinds of interest which might also claim
the title of " real " ; we refer to " labor" and " income"*
interest. It cannot even be claimed that relative
changes in prices, wages and incomes are abnormal phe-
nomena, or incident only to a dynamic society. Even
in the most ideal stationary state, the mere changes in
seasons would make interest between summer and winter
' See Chapter I, § 2.
"^ Political Science Quarterly, September, 1895.
* Professor Edgeworth ( " Variations in Value of Monetary Stand-
ards", Report of the British Association for the Advancement of
Science, 1889, p. 163), exhibits seven kinds of standards for deferred
payments.
* See Chapter X, ?? 8, 9.
90 Ama-ican Economic Association. [432
low in terms of summer precincts sncli as frnit, and high
in terms of winter products such as ice. The rate of
interest is, as Professor Bohm-Bawerk shows, an agio on
present goods exchanged for future goods of the same
kind. It is a simple corollary of this theorem, though
Professor Bohm-Bawerk does not express it, that this
agio may be in theory and must be in practice a different
agio for each separate kind of goods.
§ 2.
But, it may be urged, surely there is some invariable
standard conceivable in theory if not determinable in
practice, which may serve for a base line of apprecia-
tion and depreciation for all goods and money, and in
terms of which we may express a "real" rate of interest.
This brings us to the question of an absolute standard
of value. But here we encounter another difficulty.
Such an absolute standard will differ with each indi-
vidual.^ The fact that a dollar is a smaller unit to a
millionaire than to a poor laborer, has as its consequence
that as the millionaire grows poorer his dollar grows
larger while as the laborer grows richer his dollar grows
smaller. On account of such changes in personal for-
tunes the dollar, however defined, will be constantly
appreciating and depreciating in different degrees among
different men and classes. In fact the phenomenon of
borrowing and lending is to some extent itself a conse-
quence of the different degrees in which money appre-
ciates or depreciates to borrower and lender.
1 Marshall, "Principles," Vol. I, (3rd ed.), p. 198, and Royal Com-
mission on Depression of Trade, 1SS6, p. 423 ; also the writer's
"Mathematical Investigations in the Theory of Value and Prices,"
Transactions of the Connectictd Academy, (New Haven, 1892).
433] Appreciation and hiterest. 91
In addition to the differences already mentioned, there
is a different rate of interest for each period of time con-
sidered. The rate in any given goods for a loan con-
tracted to-day and payable one year hence is the agio of
this year's over next year's goods ; the rate for a -loan to
be contracted one year hence and payable two years
hence is the agio ( reckoned to-day ) of next year's goods
over the goods of the succeeding year and so on. The
rate for a loan contracted to-day and payable two years
hence is the " actuarial average " ^ of the two previous
rates. There is no reason why these three rates and
others constructed in the same manner should not be all
different.^
§ 4-
We thus reach a multiple theory of interest. Our
results are, first, that different standards have in general
different rates of interest ; secondly, that of the numer-
ous standards thus possible a different one is " absolute "
for each individual ; thirdly, that in each standard there
will be a different rate for dijfferent periods of time.^
' See Chapter V, § 4.
"^ Professsor Bohm-Bawerk ( "Positive Theory, " p. 280 ), in showing
how "arbitrage transactions" tend to equalize rates, tacitly assumes
that the iirst two rates above mentioned are equal and only proves
that in that case the third will be equal to the first.
^ Besides these three sorts of variations there are others due to un-
certainties of various kinds. In the theory of Part I, we have only
considered the case where the relative divergence of two standards is
foreknown with certainty. To complete the picture it is necessary to
introduce the theory of probabilities as applicable to economics.
(See Marshall's "Principles", p. 198, note, and 211, note.) When this
is done it will also explain the diiferent terms for call loans, 30 days, 60
days loans, etc., as well as for different degrees of security. Although
in the latter case we may distinguish pure interest as the rate for per-
fect security, yet the surplus above this sum is not simple insurance-
It is not a certain sum paid for a contingent loss but it is itself con-
92 American Economic Association. [434
In actual business experience none of these three sorts
of differences attract attention. The third is usually
very slight in amount. ^ The second is not reducible to
statistical measurement ; while the first escapes notice
because of the habit of reckoning- always in money. In
a few cases, as for Indian and Chinese bonds, London
brokers must have occasion to note the fact that 3% in
silver is usually not equivalent to 3 ^ in gold, but even
in such cases the gold rate is thought of as " the " rate.
So also speculative contracts in wheat, land, etc., and
ordinary loans, which are really advances of stock, ma-
terials, and other forms of capital, are always translated
into money and their essential nature as involving inde-
pendent standards is concealed. But the economist, who
so often finds it necessary to forsake the language of
money and speak in terms of the things which money
measures, must here also recognize the fact that the rate
of interest in terms of money is simply a common repre-
sentative of multiform rates in other standards.
These rates are mutually connected and our task has
been merely to state the law of that connection. We
have not attempted the bolder task of explaining the
rates themselves. Such an explanation constitutes the
" theory of interest " in the more usual sense and forms
the subject of Professor Bohm-Bawerk's masterly trea-
tise. The relation between the two branches of the sub-
ject may be pictured as somewhat analogous to that be-
tween the theory of relative prices and the theory of
price levels.
tingeut ; and, what is more important here, it is not a present sum but
a series of deferred sums and as such is itself subject to the principles
of pure interest. It follows that we cannot strike out the " insurance
element " as a mere additive term with which the theory of interest
proper has no concern. A complete theory has yet to be written.
' For a supposable case of great variation, see Chapter V, ^ ? i, 2.
APPENDIX.
STATISTICAL DATA.
§ I.
The writer has found so much difficulty in securing
a long series of yearly averages for rates on " money ",
that the results are here presented in the hope that they
may be of use to others.
YEARLY AVERAGE RATES OF INTEREST ON " MONEY." i
London
Berlin.
New York.
Calcutta
' (LI C rt I
Tokyo.
Shanghai.
1824
1825
1826
1S27
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
i860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
188 1
1882
1883
1884
1S85
1886
1887
ib88
1889
1890
1891
1892
1893
1894
1895
I 3-5
3-9
4-5
3-3
30
3-4
, 2.8
! 3-7
I 3-1
! 2.7
3-4
3-7
4.2
4-5
3-0
5-1
50
4-9
3-3
2.2
2.1
3-0
3-8
5-9
3-2
2.3
2.2
3-1
1-9
3.7
4-9
4-7
5-9
7-1
3.1
25
4.1
5-5
2.4
4-3
7-4
4.6
6.7
2.3
1.8
3-0
3-1
2.7
3-8
4-5
3-5
3-0
2.2
2.3
3-5
1.8
2.2
2.9
3-4
3-0
2.6
2.0
2-1
2.4
2.4
2.7
3-7
2.5
1-5
3-9
9-7
6.5
7.0
6.1
4-9
4.2
4.2
5-1
5-5
8.7
6.9
9-1
5-1
5.8
6.0
5-7
4-7
50
3-9
6.2
5-7
6.8
8.4
5-3
6.3
4.6
5-3
6.6
6.8
6.4
5-4
6.0
5-6
5-5
7.0
5-8
3-1
3-5
4-9
5-4
4-3
iS.
!i8
14-
18
14-
18
14.
14
12.
ii4
12.
'14
12.
i,S
10.
^3
II.
15
11. |i6
13- '17
14- ;i7
10. 17
7.9 II
12. 16
13. II
8.8 9
9.0 8
10. I 9
TO. 10
11. II
9-4 9
8.3! 8
7.8i 7
9-3; •
9.6 .
I The London, Berlin and Paris market rates are on first class merchants'
437] Appreciation arid Interest. 95
All the rates are entered in the foregoing table as
rates of "interest," though the rates for the Banks of
England, Germany and France are rates of discount.
The two are not quite equivalent but, for the purposes
of the foregoing work, the distinction between them is
unnecessary because, in a continuous series, the error, if
any, affects all items nearly alike and thus cancels itself
out in the comparisons.
Had it been necessary, some of the tables could have
been extended back. Thus the Bank of England rate
could be given to 1696 but it was too inflexible to be of
use. The Berlin and Paris bank rates could also be ex-
tended and the Paris market rate could be given from
1861 (except for 1870 and 1871) from data in Wi^ Econo-
mist.
bills. The figures for 1824-58 are from the evidence of D. B. Chapman before the
Committee on the Bank Act, 1857, Sess. 2, X, pt. I, p. 463, (also reprinted in
Hunt's Merchants' Magazine. Vol. 41, (1859) P- 95)- Th"; remaining figures are
compiled from the Economist. For those for 18S4-94, the writer is indebted to
Professor F. M. Taylor of Michigan University, who had collected them, from the
Economist for a different purpose. The Bank of England rates for 1824-43 are re-
duced from Burdett's " Ofiicial Intelligencer," (1894), p. 1,771. The remaining ones
for England, Germany and France are reduced from those given in the Report
of the Royal Commission on Depression of Trade, 1886, p. 373, and the Economist.
They represent the bank "minimum." The New York rates are taken, the first
two columns, from a table by E. B. Elliott (afterward government actuary) in
the (New York) Banker's Magazine, 1S74. The quotations given as "60 days"
apparently included single name paper. The third column to 1890 is compiled
from a diagram of highest and lowest monthly rates prepared at Yale college by
Mr. G. P. Robbins of the class of 1891, and has been completed from the Financial
Review, by averaging the highest and lowest weekly rates. It has been
found impossible to extend the table back beyond 1849, as the rates are not
systematically reported. The Calcutta rates are the minimum of the Bank of
Bengal and have been kindly furnished by Messrs. Place, Siddons and Gough,
brokers, of Calcutta. The market rates of Tokyo are averages of the highest and
lowest rates of each year, furnished by Mr. Ichi Hara of the Bank of Japan,
Tokyo. The bank rates are for the Tokyo and Yokohama Co-operative Bank and
were translated by Mr. Sakata, student at Yale, from a history of Japan by
Zenshiro Tsuboya. The tables for Shanghai have been procured through the
kindness of Mr. F. W. "Williams of the department of Oriental History of Yale
University, who obtained them from Mr. J. F. Seaman of Shanghai. The first
column contains the rates ruling in the native market, and the second, those of
the Hong Kong and Shanghai bank (under English control) on overdrawn cur-
rent accounts, a species of demand loans and the ordinary form of lending in
Shanghai. Mr. Seaman was told that the market rates cannot be extended back
beyond 1S85, as the books of the Chinese banks for previous years are burnt.
2 This rate is only from September when the operation of the Bank Act began,
previous to this the custom of the bank was to have a uniform rate for all loans.
gS American Economic Association. [438
Many of the sources from which the table has been
drawn also contain other information such as the rates
for Vienna, Amsterdam and other money centres, the
weekly or monthly rates, the variation with the seasons,
the number of changes of the Bank Minimum, etc.
§2.
Of sources not mentioned in the above note, the chief
which the writer has encountered are :
Adolf Soetbeer, " Materiallen zur Wabrungsfrage," (Berlin, 1S86),
p. 78.
Covers 1851-S5 for Banks of England, France and Germany, and mar-
ket rates of Hamburg and Vienna.
Austrian Government, " Tabellen zur Wabrungsfrage," (Vienna,
1S92), pp. 204-6. (A second edition bas just appeared, 1896).
Covers 1S61-91 for banks of Italy, England, France, Germany, Austria,
Belgium and Holland, and market rates in Vienna, iS6q-gi.
W. Stanley Jevons, " Investigations in Currency and Finance," (Lon-
don, 1884).
Contains diagram for prices of consols and 3 per cent, stock from 1731,
and minimum rate of interest in London from 1824 ; also monthly vari-
ation in rate of interest, p. 10. The diagram for the price of consols
shows that during the middle and first half of the eighteenth century
the interest realized was almost as low as in the present generation.
This was a period of falling prices.
Eleventb Census of the United Slates, Bulletin 71 (on real estate
mortgages, 1880-89).
This is probably the most elaborate series of interest averages ever
constructed. If these averages be compared with the course of prices
during the average term of the contracts (five years), it will be found
in nearly every case that interest is high or low according to the degree
of the rise or fall in prices.
"Viscomte G. D'Avenel, " Histoire economique de la propriety, des
Salaires, des Denr^es et de tous les Prix en gdn^ral depuis I'an 1200
jusqu'en I'an 1800," (Paris, 1894), vol. II, p. 882.
This work contains also tables of the purchasing power of money, but
neither the interest nor price statistics are sufficiently exact or detailed
for use in the foregoing study.
Tooke, "History of Prices," and
Tooke and Newmarcb, " History of Prices from 1793 to 1856."
G. Winter, "Zur Gescbicbte des Zinsfusses in Mittelalter," Zeit-
schrift fiir Social und Wirlschaftsgeschichte, (Weimar), 1895,1V, 2.
Arthur Crump, "English Manual of Banking," (4th ed., London,
1879). PP- Mi-4-
Gives Bank of England rates for 1694-1876.
439] Appreciation and hiterest.
97
Alph. Courtois fils, " Histoire des Banques en France," (Paris, 1881).
Gives rate of interest at the Bank of France, iSoo-1880.
Wilhelm von Lucam, " Die Oesterreichische Nationalbank wahrend
der Dauer des dritten Privilegiums," (Vienna, 1876), p. 121.
Gives rates for Bank of Austria, 1817-75.
"Jahrbiicher fiir Nationalokonomie und Statistik," February, 1896,
pp. 282-83.
Gives bank and market rates for London, Paris, Berlin, Amsterdam,
Brussels, Vienna and St. Petersburg, 1841-80 by decades, and 1881-95 by
years.
" Handworterbuch der Staatswissenschaften," Article "Banken."
Gives rates for Bank of Prussia and Germany, iS47-89i^^for Bank
of Austria, 1878-89 ; Switzerland, 1883-88. <^^^
A. N. Kiaer, " Om seddelbanker, " (Kristiania, 1877).
Contains diagram of bank rates at Kristiania, Stockholm and Kjoben-
havn, 1853-76.
M. G. Mullhall, "Dictionary of Statistics," (London, 1892), pp. 76,
607.
Gives rates for countries of Europe by five and ten year periods since
1850.
William Farr, "On the valuation of railroads, telegraphs," ^ic, Jour-
nal of the Royal Statistical Society, September, 1S76, pp. 464-530,
" Report of the New England Mutual Life Ins. Co.," Boston, 1890.
Gives rates realized by twenty representative insurance companies for
1869-88, and for Massachusetts savings banks for 1877-89, and bank divi-
dends in Boston, New York and Philadelphia. The rates realized by the
insurance companies for the twenty years, 1869-88, inclusive, were 6.0,
5.9, 6.1, 6.2, 6.5, 6.2, 6.5, 6.1, 5.6, 5.1, 5.0, 4.8, 4.8, 5.1, 5.1, 4.7, 4.7, 4.9, 4.7, 4.6,
respectively. These represent (if the -writer mistakes not) the average
rates earned on the par value of investments of all ages, some old, some
new, some terminable soon and others having many years to run. For
this reason they are of little or no use for the foregoing study.
Robert GifFen, "Essay in Finance," second series, (London, 1886),
P- 37-
Seasonal variations of interest in connection with bank reserves, etc.
F. M. Taylor, ' ' Do we want an Elastic Currency ? ' ' Political Science
Quarterly, March, 1896, pp. 133-157.
Gives diagram showing the relation of surplus reserves and rates of
discount ; also seasonal variation of rate of discount.
R. H. Inglis Palgrave, "Analysis of the Transactions of the Bank of
England," (London, 1874).
Gives rates, 1844-72, and seasonal variation, 1844-56 and 1857-72. Shows
dependence of rate on ratio of reserve to liabilities.
R. H. Inglis Palgrave, "Bank-rate in England, France, and Germany,
1844-78 ; with remarks on the causes which influence the rate of
interest charged ; and an analysis of the accounts of the Bank of
England," (London, 1880).
R. H. Inglis Palgrave, (London) Bankers' Magazine, March, April,
May, 1878.
Number of changes in bank rates of England, France, and Germany.
^8 American Economic Association. [446
Theodor Hertzka, "Wahrung und Handel," (Vienna, 1S76).
Gives the number of weeks each rate lasted for the Banks of England,
France, Germany, and Austria during 1844-73.
George Clare, "Money Market Primer," (London, 1S91).
Diagrams for seasonal variations of interest, bank reserves, etc.
Commercial and Financial Statistics of British India. Second issue,
(Government Printing OfSce, Calcutta), 1894, pp. 354-64.
Monthly Discount, Bank of Bengal, 1861-94, and average quotations of
government securities held in I,ondon.
Report of the Secretary of the Treasury, 1893, p. 401.
Report of the Comptroller of Currency, 1894, p. 179.
H. W. Farnam, "Some Effects of Falling Prices," Yale Review, Au-
gust, 1895.
The last three references contain statistics of rates of interest realized
on some United States Government bonds.
R. A. Bayley, "National Loans of the United States", (Government
Printing Ofl&ce, Washington, 1882).
Gives rates of interest and price of issue of all United States loans from
July 4, 1776, to June 30, 1880.
"Dictionaire des Finances," Article "Interet."
Gives rates at vrhich France has borrowed.
The following tables of index numbers are appended
in order that the reader may verify the periods of rising
and falling prices which have been discussed in Chapters
X and for the reason that many of the tables, notably
those for India, Japan and China, have not hitherto
been accessible to most readers.
INDSX NUMBERS IN SEIVEN COUNTRIES.i
England.
1824
1825
1826
1827
182S
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
i860
1861
1852
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
188 1
1882
1883
1884
1885
1886
1887
1890
1891
1892
1893
1894
1895
105
124
108
108
97
95
97
98
93
90
93
96
103
lOI
loi
no
104
102
90
85
83
94
82
77
77
79
781
95
102
loi
lOI
105
91
94
99
98
lOI
103
105
lOI
102
100
99
98
96
100
109
III
102
96
95
94
87
113
134
129
Germany.
100
102
114
121
124
123
130
114
116
121
118
123
125
129
123
126
124
122
123
123
127
136
138
136
130
128
128
121
117
122
121
122
122
114
109
104
102
102
106
108
109I
106
102
92
91
United States.
100
118
127
129
112
115
100
95
97
94
94
105
103
94
87
85
82
79
90
84
85
88
95
95
88
83
89
99
98
105
105
109
112
114
"3
103
100
94
104
132
172
232
188
166
174
152
144
136
132
129
130
129
123
114
105
95
105
108
109
107
103
93
93
94
96
98
94
94
83
100
100
loi
104
119
134
149
156
164
165
167
167
166
167
166
162
158
151
144
141
139
143
151
153
159
155
156
156
157
158
163
168
169
India.
95
99
121
125
119
112
99
96
97
95
99
loi
104
107
103
104
"5
119
Japan.
104
104
105
102
105
114
145
160
175
159
130
116
116
107
109
112
116
124
123
124
129
China.
100
103
III
10 1
106
III
105
no
108
103
104
105
107
105
100
105
104
104
108
109
1 For England, the figures for prices are from Jevons and Sauerbeck. Those
lOO American Economic Associatio7i. [442
from Sauerbeck begin in 1852. They are taken from the Aldrich report (I, 247)
and from the Journal of the Royal Statistical Society, March, 1S96. Those from
Jevons are from 1824 to 1852 inclusive, and are taken from his " Investigitions in
Currency and Finance." In order to make ihe tables of Jevons and Sauerbeck
continuous, Jevons' number for 1S52 is called 78 (i. e., Sauerbeck's for that year)
instead of 65 as given in the "Investigations," and all the other numbers are
raised in the ratio 78 : 65. Jevons' figures are for forty commodities ; Sauerbeck's
for fortj'-five. The index numbers for English wages are from the article by
Bowley in the Journal of the Royal Statistical Soceety, June, 1895.
The German numbers are from Soetbeer, Heinz and Conrad. Those for 1851-gi
inclusive, are from Soetbeer, continued by Heinz, and given in the Aldrich report
(I, 294) ; those for 1891-95 inclusive, are from Conrad, as given in "his JahrbUcher^
1S94-6, but are all magnified in the ratio 109 : 98 in order to make the series con-
tinuous, since Heinz's figure for 1891 is 109, and Conrad's 98. The statistics of
Soetbeer and Heinz cover 114 commodities.
The French numbers are from the Aldrich report (I, 335) founded on the figures
of the Commission permanente des valeurs. They cover only sixteen articles.
The figures for the United States are those of Professor Falkner in the Aldrich
report (I, 9, 13), the weighted averages (last method) being employed.
Those for India, Japan and China are from the Japanese Report of the Com-
mission for investigation of monetary systems, 1S95. The writer is under great
obligations to Mr. Ichi Hara, of Tokyo, for a copy of the report, and to Mr.
Sakata of Yale University, for translating the tables.
That for India is an average of three tables which cover respectively twentj'-one
articles of export, sixteen articles of export priced at Calcutta and Bombay, and
eight grains at Bombay. That for Japan is an average of three tables, of forty-
two articles at Tokyo, sixteen at Osaka and thirty. one articles of export. That
for China is an average of three tables, of twenty inland commodities, seventeen
articles of export and fifteen food-stuffs in Shanghai.
The tables for India were based on official statistics, those for Japan on in-
formation from guilds and merchants, and those for China on the reports of the
consuls of Japan and England (Mr. Jameson) in China.
In the Japanese report the prices for Japan are reduced to a silver basis. As
silver was at a premium up to 1S85 it has been necessary in constructing the
above table to reconvert into currency by applj'ing the premium for 1873-85, viz.:
4, 4i 3) I1 3) 10) 32, 48, 70, 57, 26, 9, 5 per cent, respectively.
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